Chapter 4: Linear Functions and Relations · OBJ: 4-1.1 Write and graph linear equations in...
Transcript of Chapter 4: Linear Functions and Relations · OBJ: 4-1.1 Write and graph linear equations in...
Chapter 4: Linear Functions and Relations
MULTIPLE CHOICE
Write an equation of the line with the given slope and y-intercept
1. slope: 2
7, y-intercept: –3
a. y = 2
7x – 3 c. y =
2
7x + 3
b. y = 7
2x – 3 d. y =
2
7x – 3
ANS: D
The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the
y-intercept.
Feedback
A What is the slope of the line? B What is the slope? C What is the y-intercept? D Correct!
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 STA: OK 2.3 | OK 2.5a | OK 2.5b
TOP: Write and graph linear equations in slope-intercept form
KEY: Slope-Intercept Form | Linear Equations | Graphs
2. slope: 0.8, y-intercept: 10
a. y = –0.8x + 10 c. y = 0.8x + 10
b. y = 0.8x – 10 d. y = 5
7x + 10
ANS: C
The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the
y-intercept.
Feedback
A What is the slope? B What is the y-intercept? C Correct! D What is the slope of the line?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.1 Write and graph linear equations in slope-intercept form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 4 STA: OK 2.3 | OK 2.5a | OK 2.5b
TOP: Write and graph linear equations in slope-intercept form
KEY: Slope-Intercept Form | Linear Equations | Graphs
Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle.
3. Write an equation for the total cost C of renting a bicycle and riding for m miles.
a. c.
b. d.
ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Correct! B Which number would be the y-intercept in the linear equation? C Which variable should be the independent variable? D What is the rate of change?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
4. Graph the equation needed to represent the cost at Beach Bike Rentals.
a.
1 2 3 4 5 6 7 8 9 10 m
1
2
3
4
5
6
7
8
9
10C
b.
1 2 3 4 5 6 7 8 9 10 m
1
2
3
4
5
6
7
8
9
10C
c.
1 2 3 4 5 6 7 8 9 10 m
1
2
3
4
5
6
7
8
9
10C
d.
1 2 3 4 5 6 7 8 9 10 m
1
2
3
4
5
6
7
8
9
10C
ANS: B
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Is the rate of change positive or negative? B Correct! C What is the y-intercept? D What is the base rental cost?
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
5. What is the cost of renting a bike and riding 18 miles?
a. $3.60 c. $8.60
b. $41.00 d. $11.60
ANS: C
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Did you forget the base rate for bike rental? B What is the rate per mile? C Correct! D What was the base rate for bike rental?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
Write a linear equation in slope-intercept form to model the situation.
6. A television repair shop charges $35 plus $20 per hour.
a. c. b. d.
ANS: D
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Which number represents the intercept? B Which variable is the independent variable? C What is the slope? D Correct!
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
7. An icicle is 12 inches long and melts at a rate of inch per hour.
a. c.
b. d.
ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Correct! B What was the original length of the icicle? C What is the rate of change? D Which variable is the independent variable?
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
8. The temperature is 38 and is expected to rise at a rate of 3 per hour.
a. c. b. d.
ANS: B
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A What is the starting temperature? B Correct! C Is the temperature decreasing? D Which variable is the independent variable?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
9. A taxi driver charges $5 plus $0.30 per mile.
a. c. b. d.
ANS: C
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A What is the base price? B Does the cost go down with additional miles? C Correct! D Which variable is the independent variable?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to
add 8 sections each Saturday until he is finished.
10. Write an equation to find the total number of fence sections F standing after any number of
Saturdays s.
a. c. b. d.
ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Correct! B How many sections are already up? C Does the number of sections standing decrease each Saturday? D Which variable is the independent variable?
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
11. Graph the equation for the number of fence sections F standing after any number of Saturdays s.
a.
Saturdays
Fen
ce S
ections
1 2 3 4 5 6 7 8 9 10 s
10
20
30
40
50
60
70
80
90
100
110
F
b.
Saturdays
Fen
ce S
ections
1 2 3 4 5 6 7 8 9 10 s
10
20
30
40
50
60
70
80
90
100
110
F
c.
Saturdays
Fen
ce S
ections
1 2 3 4 5 6 7 8 9 10 s
10
20
30
40
50
60
70
80
90
100
110
F
d.
Saturdays
Fen
ce S
ections
1 2 3 4 5 6 7 8 9 10 s
10
20
30
40
50
60
70
80
90
100
110
F
ANS: A
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A Correct! B What is the y-intercept? C Does the number of sections standing decrease each Saturday? D What is the slope of the line?
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
12. Find the total number of fence sections standing after 15 Saturdays.
a. 383 sections c. 145 sections
b. 125 sections d. 105 sections
ANS: C
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
Feedback
A How many sections did he install each Saturday? B How many sections were standing at the beginning? C Correct! D How many Saturdays did you use?
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.2 Model real-world data with an equation in slope-intercept form.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Model real-world data with an equation in slope-intercept form
KEY: Slope-Intercept Form | Equations | Real-World Problems
Write an equation of the line that passes through each point with the given slope.
13.
a. c.
b. d.
ANS: D
Find the y-intercept by replacing x and y with the given point and m with the given slope in the
slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the
calculated b.
Feedback
A What is the y-intercept? B What is the y-intercept? C What is the slope of the line? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.1 Write an equation of a line given the slope and one point on the line.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Write an equation of a line given the slope and one point on a line
KEY: Slope | Equations | Lines
14.
a. c.
b. d.
ANS: B
Find the y-intercept by replacing x and y with the given point and m with the given slope in the
slope-intercept form. Solve for b. Write the equation in slope-intercept form using the given m and the
calculated b.
Feedback
A What is the slope of the line? B Correct!
C What is the y-intercept? D What is the y-intercept?
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.1 Write an equation of a line given the slope and one point on the line.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Write an equation of a line given the slope and one point on a line
KEY: Slope | Equations | Lines
Write an equation of the line that passes through the pair of points.
15.
a. y = 1
8x +
11
8 c. y =
1
8x –
11
8
b. y = 1
8x –
11
8 d. y =
1
8x +
8
11
ANS: B
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
Feedback
A What is the y-intercept? B Correct! C Is the slope positive or negative? D How did you find the y-intercept?
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.2 Write an equation of a line given two points on the line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b
TOP: Write an equation of a line given two points on the line KEY: Slope | Lines | Equations
16.
a. y = –8x + 22 c. y = 8x – 32
b. y = –8x + 32 d. y = –8x – 32
ANS: D
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
Feedback
A How did you find the y-intercept? B What is the y-intercept? C Is the slope positive or negative? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.2 Write an equation of a line given two points on the line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b
TOP: Write an equation of a line given two points on the line KEY: Slope | Lines | Equations
Write the point-slope form of an equation for a line that passes through the point with the given slope.
17. (–4, 3), m = 1
a. y – 3 = 1(x + 4) c. y – 3 = 1(x – 4)
b. y + 3 = 1(x + 4) d. y – 3 = –(x + 4)
ANS: A
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Feedback
A Correct! B What is the y-coordinate of the given point? C Did you subtract the x-coordinate from x? D What is the slope of the line?
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Write the equation of a line in point-slope form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4c
TOP: Write the equation of a line in point-slope form
KEY: Point-Slope Form | Equations | Lines
18. (–6, –6), m = 4
7
a. y – 6 = 4
7(x + 6) c. y + 6 =
4
7(x + 6)
b. y + 6 = 4
7(x – 6) d. y + 6 =
4
7(x + 6)
ANS: D
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Feedback
A What is the y-coordinate of the given point? B Did you subtract the x-coordinate from x? C What is the slope of the line? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.1 Write the equation of a line in point-slope form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4c
TOP: Write the equation of a line in point-slope form
KEY: Point-Slope Form | Equations | Lines
Write each equation in standard form.
19. y + 6 = (x + 4)
a. x + y = –2 c. x – y = 2
b. y = x – 2 d. x – y = 10
ANS: C
Solve the equation for y. Use Addition and Subtraction Properties of Equality to rewrite the equation in
standard form.
Feedback
A How did you determine the sign of the y-term? B Is that standard form? C Correct! D Did you use the correct property of equality?
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Write linear equations in standard form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write linear equations in standard form
KEY: Standard Form | Linear Equations
20. y + 3 = 2
5(x + 9)
a. 2x – 5y = 33 c. y = 2
5x +
3
5
b. 2x – 5y = –3 d. 2x + 5y = 3
ANS: B
Solve the equation for y. Use Addition and Subtraction Properties of Equality to rewrite the equation in
standard form.
Feedback
A Did you use the correct property of equality? B Correct! C Is that standard form? D How did you determine the sign of the y-term?
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.2 Write linear equations in standard form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write linear equations in standard form
KEY: Standard Form | Linear Equations
Write the equation in slope-intercept form.
21.
a. c.
b. d.
ANS: B
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
Feedback
A What is the slope of the line? B Correct!
C How did you find the y-intercept? D What is the y-intercept of the equation?
PTS: 1 DIF: Basic REF: Lesson 4-3
OBJ: 4-3.3 Write linear equations in slope-intercept form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write linear equations in slope-intercept form
KEY: Slope-Intercept Form | Linear Equations
22. y – 5 = 3
4(x – 5)
a. y = 3
4x –
5
4 c. y =
3
4x +
5
4
b. y = 3
4x +
5
4 d. y =
3
4x –
3
5
ANS: B
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
Feedback
A What is the y-intercept of the equation? B Correct! C What is the slope of the line? D How did you find the y-intercept?
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.3 Write linear equations in slope-intercept form.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write linear equations in slope-intercept form
KEY: Slope-Intercept Form | Linear Equations
Write the slope-intercept form of an equation of the line that passes through the given point and is
parallel to the graph of the equation.
23. (5, –1), y = 3
4x + 1
a. y = 11
4x +
3
4
b. y = 4
3x +
11
5
c. y = 3
4x +
11
4
d. y = 3
4x –
11
4
ANS: C
Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the
parallel line in the point-slope form. Then change to the slope-intercept form.
Feedback
A What is the slope of the parallel line? B Did you add or subtract carefully? Should the slope be the same as the slope of the
parallel line? C Correct!
D Be careful with signs when adding to or subtracting from both sides of the equation.
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.1 Write an equation of the line that passes through a given point, parallel to a given line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write an equation of the line that passes through a given point, parallel to a given line
KEY: Lines | Equations | Parallel
24. (–5, –3), 5x – 4y = 8
a. y = 5
4x +
13
4
b. y = 5
4x –
13
4
c. y = 4
5x +
13
5
d. y = 13
4x +
5
4
ANS: A
Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the
parallel line in the point-slope form. Then change to the slope-intercept form.
Feedback
A Correct! B Be careful with signs when adding to or subtracting from both sides of the equation. C Did you add or subtract carefully? Should the slope be the same as the slope of the
parallel line? D What is the slope of the parallel line?
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.1 Write an equation of the line that passes through a given point, parallel to a given line.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c
TOP: Write an equation of the line that passes through a given point, parallel to a given line
KEY: Lines | Equations | Parallel
Write the slope-intercept form of an equation that passes through the given point and is perpendicular
to the graph of the equation.
25. (4, 4), 2x – y = 4
a. y = 2x + 2
b. y = 1
2x + 6
c. y = 1
2x + 6
d. y = 4x + 2
ANS: B
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the
given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept
form.
Feedback
A Did you add or subtract carefully? Should the slope be the same as the slope of the
perpendicular line?
B Correct! C How are the slopes of perpendicular lines related? D What is the slope of the perpendicular line?
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.2 Write an equation of the line that passes through a given point, perpendicular to a given
line. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Write an equation of the line that passes through a given point, perpendicular to a given line
KEY: Lines | Equations | Perpendicular
26. (2, 2), y = 1
5x + 5
a. y = 1
5x – 2
b. y = 5x – 8
c. y = 5x – 8
d. y = 12
5x –
1
5
ANS: B
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the
given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept
form.
Feedback
A Did you add or subtract carefully? Should the slope be the same as the slope of the
perpendicular line? B Correct! C How are the slopes of perpendicular lines related? D What is the slope of the perpendicular line?
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.2 Write an equation of the line that passes through a given point, perpendicular to a given
line. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Write an equation of the line that passes through a given point, perpendicular to a given line
KEY: Lines | Equations | Perpendicular
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If
there is a positive or negative correlation, describe its meaning in the situation.
27.
Women in the Army
Per
cent
1981 1991 2001
2
4
6
8
10
12
14
16
Year
Source: Time Magazine, March 24, 2003
a. positive; as time goes on, more women are in the army.
b. no correlation
c. negative; as time goes on, fewer women are in the army.
d. negative; as time goes on, more women are in the army.
ANS: A
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Correct! B Are the variables related? C Is the number of women in the army decreasing? D What is meant by negative correlation?
PTS: 1 DIF: Basic REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
28.
Average Cycling Speed
Mil
es P
er H
our
M inutes5 10 15 20 25 30 35
2
4
6
8
10
12
14
16
18
a. no correlation
b. negative; as time passes, speed decreases
c. positive; as time passes, speed increases
d. positive; as time passes, speed decreases
ANS: B
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Are the variables related? B Correct! C Is the speed increasing? D What is meant by positive correlation?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
29.
Video Rental Fines
Fin
es (
do
llar
s)
Videos Rented1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
a. negative; as the number of videos rented increases, the amount of fine increases.
b. negative; as the number of videos rented increases, the amount of fine decreases.
c. no correlation
d. positive; as the number of videos rented increases, the amount of fine decreases.
ANS: C
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A What is meant by negative correlation? B Does the amount of fine decrease with the number of videos rented? C Correct! D What is meant by positive correlation?
PTS: 1 DIF: Basic REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
30.
People Entering Amusement Park
Num
ber
of
Peo
ple
10 20 30 40 50 60 70 80 90 100
100
200
300
400
500
600
700
800
900
1000
Time (minutes)
a. positive; as time passes, the number of people entering decreases.
b. negative; as time passes, the number of people entering decreases.
c. no correlation
d. positive; as time passes, the number of people entering increases.
ANS: D
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A What is meant by positive correlation? B Does the number of people decrease as time passes? C Are the variables related? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
31.
Strawberries Picked
Quar
ts P
icked
1 2 3 4 5 6 7 8 9 10
10
20
30
40
50
60
70
80
90
100
Time (hours)
a. positive; as time passes, the number of quarts picked decreases.
b. negative; as time passes, the number of quarts picked decreases.
c. no correlation
d. positive; as time passes, the number of quarts picked increases.
ANS: B
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A What is meant by positive correlation? B Correct! C Are the variables related? D Does the number of quarts picked increase over time?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
32.
United States Birth Rate (per 1000)
1990 1992 1994 1996 1998 2000
12
14
16
18
20
22
24
Year
Source: National Center for Health Statistics, U.S.
Dept. of Health and Human Services
a. no correlation
b. positive correlation; as time passes, the birth rate increases.
c. positive correlation; as time passes, the birth rate decreases.
d. negative correlation; as time passes, the birth rate decreases.
ANS: D
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Are the variables not related? B Is the birth rate increasing with the passage of time? C What is mean by a positive correlation? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
33.
Consumer Price Index, 1950-2002
1950 1960 1970 1980 1990 2000
100
200
300
400
500
600
700
Year Source: Bureau of Labor Statistics, U.S. Dept. of Labor
a. no correlation
b. positive correlation; as time passes, the CPI increases.
c. positive correlation; as time passes, the CPI decreases.
d. negative correlation; as time passes, the CPI decreases.
ANS: B
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Are the variables not related? B Correct! C What is meant by positive correlation? D Is the CPI decreasing?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
34.
Sport Utility Vehicle Sales in the U.S.,
1991-2001
1990 1992 1994 1996 1998 2000 2002
1
2
3
4
5
6
7
Year Source: The World Almanac, 2003
a. negative correlation; as time passes, SUV sales decrease.
b. no correlation
c. positive correlation; as time passes, the SUV sales decrease.
d. positive correlation; as time passes, the SUV sales increase.
ANS: D
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Are sales decreasing? B Are the variables not related? C What is meant by positive correlation? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
35.
Domestic Traveler Spending in the U.S., 1987-1999
1986 1988 1990 1992 1994 1996 1998
225
250
275
300
325
350
375
400
425
450
Year Source: The World Almanac, 2003
a. positive correlation; as time passes, spending increases.
b. no correlation
c. positive correlation; as time passes, spending decreases.
d. negative correlation; as time passes, spending decreases.
ANS: A
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A Correct! B Are the variables not related? C What is meant by positive correlation? D Is spending decreasing with time?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
36.
Cars Passing School
Num
ber
of
Car
s
Hours1 2 3 4 5 6 7 8 9 10
10
20
30
40
50
60
70
80
90
100
a. negative; as time passes, the number of cars increases.
b. negative; as time passes, the number of cars decreases.
c. no correlation
d. positive; as time passes, the number of cars decreases.
ANS: C
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when as x increases, y increases. There is a negative correlation when as
x increases, y decreases. There is no correlation when x and y are not related.
Feedback
A What is meant by negative correlation? B Is the number of cars decreasing with the passage of time? C Correct! D What is meant by positive correlation?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.1 Interpret points on a scatter plot.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 3 STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a
TOP: Interpret points on a scatter plot KEY: Scatter Plot | Interpret Data
United States Birth Rate
Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Birth Rate
(per 1000)
16.7
16.3
15.9
15.5
15.2
14.8
14.7
14.5
14.6
14.5
14.7
14.5 Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
37. Let x represent the number of years since 1990 with x = 0 representing 1990. Let y represent the birth
rate per 1000 population. Write the slope-intercept form of the equation for the line of fit using the
points representing 1992 and 2000.
a. c.
b. d.
ANS: A
If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line
describes the trend of the data. Once you have a line of fit, you can find an equation of the line using 2
points to find the slope and y-intercept.
Feedback
A Correct! B Is there a positive correlation? C Did you subtract when you should have added? D Which variable is the independent variable?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
38. Predict the birthrate in 2005. Round your answer to the nearest tenth, if necessary.
a. 14.5 c. 15.1
b. 13.1 d. 14.0
ANS: D
Write an equation for the line of fit. Substitute to find a prediction for 2005.
Feedback
A Do you predict that the rate will remain unchanged from 2001? B Did you write an equation for the line of fit? C Do you predict the rate will increase from 2001? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
Domestic Traveler Spending in the U.S., 1987-1999
1986 1988 1990 1992 1994 1996 1998 2000
225
250
275
300
325
350
375
400
425
450
Year Source: The World Almanac, 2003
39. Use the scatter plot that shows the domestic traveler spending. Use the points (1987, 235) and
(1999, 446) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
a. c.
b. d.
ANS: C
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points.
Feedback
A Is the slope of the line of fit negative? B Which variable is the independent variable? C Correct! D How did you determine the slope of the line?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
40. Use the scatter plot that shows the domestic traveler spending. Predict the amount of spending for
domestic travelers in 2010.
a. about $640,000,000 c. about $640
b. about $460,000,000,000 d. about $640,000,000,000
ANS: D
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points.
Feedback
A How do you read that amount? B Do you expect the amount of spending to decrease? C Did you read the graph carefully? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
Strawberries Picked
Quar
ts P
icked
Time (hours)1 2 3 4 5 6 7 8 9 10
10
20
30
40
50
60
70
80
90
100
41. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Use the points
(1, 73) and (8, 41) to write the slope-intercept form of an equation for the line of fit shown in the
scatter plot.
a. c.
b. d.
ANS: D
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points.
Feedback
A Is the slope of the line of fit positive? B Which variable is the independent variable? C How did you determine the slope of the line? D Correct!
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
42. Use the scatter plot that shows the number of quarts of strawberries picked each hour. Predict the
number of quarts that will be picked in the tenth hour.
a. about 123 quarts c. about 32 quarts
b. about 45 quarts d. about 34 quarts
ANS: C
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points. Use the equation to make the prediction.
Feedback
A What is the slope in your equation? B Do you expect the number quarts to increase? C Correct! D Did you evaluate the equation carefully?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
Average Cycling Speed
Mil
es P
er H
our
M inutes5 10 15 20 25 30 35
2
4
6
8
10
12
14
16
18
43. Use the scatter plot that shows the average cycling speed as time passes. Use the points (5, 15) and
(25, 10) to write the slope-intercept form of an equation for the line of fit shown in the scatter plot.
a. c.
b. d.
ANS: A
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points.
Feedback
A Correct! B Which variable is the independent variable? C Is the slope of the line of fit positive? D How did you determine the slope of the line?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
44. Use the scatter plot that shows the average cycling speed as time passes. Predict the speed of the
cyclist after 30 minutes.
a. about 6.2 miles per hour c. about 12.3 miles per hour
b. about 8.8 miles per hour d. about 10.5 miles per hour
ANS: B
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points. Use the equation to make the prediction.
Feedback
A What is the slope in your equation? B Correct! C Do you expect the number quarts to increase? D Did you evaluate the equation carefully?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
Sport Utility Vehicle Sales in the U.S., 1991-2001
Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Sales
(millions)
0.9
1.2
1.4
1.6
1.8
2.2
2.5
2.8
3.0
3.4
3.8 Source: The World Almanac, 2003
45. Let x represent the number of years since 1990. Let y represent the sport utility vehicle sales in
millions. Write the slope-intercept form of the equation for the line of fit using the points representing
1992 and 2000.
a. c.
b. d.
ANS: A
If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line
describes the trend of the data. Once you have a line of fit, you can find an equation of the line using 2
points to find the slope and y-intercept.
Feedback
A Correct! B Is there a negative correlation? C Did you add when you should have subtracted? D Which variable is the independent variable?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
46. Predict the number of sport utility vehicle sales in 2005.
a. about 3.5 million c. about 2.4 million
b. about 4.8 million d. about 5.9 million
ANS: B
Use the two points to calculate the slope of the line. Then find the slope intercept form of the equation
of the line using the slope and one of the points. Use the equation to make the prediction.
Feedback
A Do you expect sales to decline? B Correct! C What is the y-intercept? D What did you find to be the y-intercept?
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.2 Use lines of fit to make and evaluate predictions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 STA: OK 2.1a | OK 2.2 | OK 2.3 | OK 2.4e | OK 3.1a
TOP: Write equations for lines of fit KEY: Best Fit Line | Equations
Find the equation of the regression line.
47.
a. c.
b. d.
ANS: B PTS: 1 DIF: Basic REF: Lesson 4-6
OBJ: 4-6.1 Write equations of best-fit lines using linear regression.
STA: OK 3.1c TOP: Regression and median fit lines.
KEY: linear regression | best-fit line
Find y for the given value of x.
48. The best-fit line is . .
a. 8.55 c. 1.2
b. 8.05 d. 7.23
ANS: A PTS: 1 DIF: Basic REF: Lesson 4-6
OBJ: 4-6.1 Write equations of best-fit lines using linear regression.
STA: OK 3.1c TOP: Regression and median fit lines.
KEY: linear regression | best-fit line
Find the graph of the function.
49.
a.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
d.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
ANS: A PTS: 1 DIF: Basic REF: Lesson 4-7
OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.
KEY: absolute value function
50.
a.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
c.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
b.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
d.
2 4 6 8 10–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
ANS: C PTS: 1 DIF: Basic REF: Lesson 4-7
OBJ: 4-7.1 Identify and graph absolute value functions. TOP: Special functions.
KEY: absolute value function
SHORT ANSWER
1. Cindy started her bank account with $400, and she deposited $50 per week. Write a linear equation in
slope-intercept form to find the total amount in her account after w weeks. Then graph the equation.
ANS:
;
Am
ou
nt
($)
1 2 3 4 5 6 7 8 9 10 x
350
400
450
500
550
600
650
700
750
800
y
Week
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
2. The cost of admission to an amusement park is $9.50 plus $1.50 per ride. Write a linear equation in
slope-intercept form for the amount spent if r rides are taken.
ANS:
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
PTS: 1 DIF: Basic REF: Lesson 4-1
OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
3. Anthony is reading a book with 256 pages. He reads 14 pages every day. Write a linear equation in
slope-intercept form to find the number of pages left after d days.
ANS:
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
PTS: 1 DIF: Average REF: Lesson 4-1
OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
4. The monthly telephone bill consists of $24 service charge plus $1.20 per call. Write an equation in
slope-intercept form for the total monthly bill if x represents the number of calls made in a month.
Then graph the equation.
ANS:
;
Number of Calls
Month
ly B
ill ($
)
20 40 60 80 100 120 140 160 180 x
40
80
120
160
200
240
280
320
360
400y
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
5. The cost, C, of joining the sports center gym includes an initial membership fee of $139 plus a $29
monthly fee. Write an equation in slope-intercept form to find the total cost for m months. Then graph
the equation.
ANS:
;
Co
st (
$)
1 2 3 4 5 6 7 8 9 10 x
100
150
200
250
300
350
400
450
500
550
y
Month
If a quantity changes at a constant rate over time, it can be modeled by a linear equation. The
y-intercept represents a starting point, and the slope represents the rate of change.
PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.3 Solve multi-step problems. NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
6. The table of ordered pairs shows the coordinates of the two points on the graph of a line.
x y
0 6
4 10
Write an equation that describes the line.
ANS:
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Basic REF: Lesson 4-2
OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
7. Write an equation and describe the slope for the line that passes through and .
ANS:
;
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
8. In 1992, about 12.5 million people were using broadband internet services. In 1999, the number was
17.4 million. Write a linear equation to predict the number of people, P, who will be using broadband
internet services in year t.
ANS:
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Advanced REF: Lesson 4-2
OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
9. Write an equation for the line that passes through and . What is the slope?
ANS:
; 2
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Average REF: Lesson 4-2
OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
10. A company manufactured 324,000 computers in 2002. The company’s output grows by 5,000 units per
year.
Year Production (thousands)
2002 324
2003 329
2004 334
Write a linear equation to find the company’s production, P, in year, t.
ANS:
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
PTS: 1 DIF: Advanced REF: Lesson 4-2
OBJ: 4-2.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
11. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that
passes through with slope 4.
ANS:
; ;
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
The linear equation in standard form is given as , where A, B, and C are constants. Use
Addition and Subtraction Properties of Equality to rewrite the equation in standard form.
PTS: 1 DIF: Basic REF: Lesson 4-3
OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
12. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that
passes through with slope –9.
ANS:
; ;
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
The linear equation in standard form is given as , where A, B, and C are constants. Use
Addition and Subtraction Properties of Equality to rewrite the equation in standard form.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
13. Write the point-slope form, slope-intercept form, and standard form of an equation for a line that
passes through with slope .
ANS:
; ;
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
The linear equation in standard form is given as , where A, B, and C are constants. Use
Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember
that A, B, and C must be integers with a GCF of 1.
PTS: 1 DIF: Advanced REF: Lesson 4-3
OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
14. Line l passes through with slope . Write the point-slope form, slope-intercept form, and
standard form of an equation for line l.
ANS:
; ;
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
The linear equation in standard form is given as , where A, B, and C are constants. Use
Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember
that A, B, and C must be integers with a GCF of 1.
PTS: 1 DIF: Average REF: Lesson 4-3
OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
15. A line passes through with slope . Write the point-slope form, slope-intercept form, and
standard form of an equation for line l.
ANS:
; ;
The linear equation is written in point-slope form, where is a given point
on a nonvertical line and m is the slope of the line.
Given an equation in point-slope form, solve the equation for y to find the equation in slope-intercept
form.
The linear equation in standard form is given as , where A, B, and C are constants. Use
Addition and Subtraction Properties of Equality to rewrite the equation in standard form. Remember
that A, B, and C must be integers with a GCF of 1.
PTS: 1 DIF: Advanced REF: Lesson 4-3
OBJ: 4-3.4 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Solve multi-step problems.
KEY: Multi-step | Problem Solving
16. Determine whether and are perpendicular. Explain.
ANS:
No; the slopes are 4 and .
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other.
PTS: 1 DIF: Basic REF: Lesson 4-4
OBJ: 4-4.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
17. Write an equation of the line that is parallel to the graph of and passes through .
ANS:
Two nonvertical lines are parallel if they have the same slope. Use the given point with the slope of the
parallel line in the point-slope form. Then change to the slope-intercept form.
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
18. Find an equation for the line that has an x-intercept of 3 and is perpendicular to the graph of
.
ANS:
or
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the
given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept
form.
PTS: 1 DIF: Average REF: Lesson 4-4
OBJ: 4-4.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
19. Determine the relationship between the diagonals and of rhombus PQRS with ,
, , and .
ANS:
They are perpendicular because the slopes are and .
Two nonvertical lines are parallel if they have the same slope.
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other.
PTS: 1 DIF: Advanced REF: Lesson 4-4
OBJ: 4-4.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
20. Write the slope-intercept form of an equation for the line that passes through and is
perpendicular to the graph of the equation .
ANS:
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other. Use the
given point with the slope of the perpendicular line in point-slope form. Then change to slope-intercept
form.
PTS: 1 DIF: Advanced REF: Lesson 4-4
OBJ: 4-4.3 Solve multi-step problems. NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
The table shows the age of infants, t (in weeks), and the number of hours, h, they slept in a day.
21. Draw a scatter plot and determine what relationship exists, if any, in the data.
ANS:
Sle
ep (
ho
urs
per
day
)
3 6 9 12 15 18 21 24 t
13
13.5
14
14.5
15
15.5
16
16.5
h
Age (in weeks)
Negative correlation.
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when y increases as x increases. There is a negative correlation when y
decreases as x increases. There is no correlation when x and y are not related.
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.3 Solve multi-step problems. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
22. Suppose a child is 2 years old. Would the equation for the line of fit give a reasonable estimate of the
number of hours slept in a day by a child of that age? Explain.
ANS:
No; using the equation would give 2.82 hrs of sleep in a day, which is not a reasonable estimate for a
2-year-old.
Write an equation for the line of fit. Use the equation to make the prediction.
PTS: 1 DIF: Average REF: Lesson 4-5
OBJ: 4-5.3 Solve multi-step problems. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
23. The table below shows Alex’s best time for the 200-m sprint each year.
Draw a scatter plot and determine what relationship, if any, exists in the data.
ANS:
Tim
e (s
)
1989 1990 1991 1992 1993 1994 1995 1996 x
28
29
30
31
32
33
34
35
36
37
y
Year
Positive correlation
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when y increases as x increases. There is a negative correlation when y
decreases as x increases. There is no correlation when x and y are not related.
PTS: 1 DIF: Basic REF: Lesson 4-5
OBJ: 4-5.3 Solve multi-step problems. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
24. The graph below shows the relationship between a long-distance truck driver’s driving times and the
number of miles traveled.
Dis
tan
ce t
rav
eled
(m
i)
60 75 90 105 120 135 150 165 180 x
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
y
Driving time (h)
Is it reasonable to use the equation for line of fit to estimate the distance traveled for a driving time of
10 hours? Explain.
ANS:
No; using the equation would give –333.3 miles, which is not a reasonable estimate.
Write an equation for the line of fit. Use the equation to make the prediction.
PTS: 1 DIF: Advanced REF: Lesson 4-5
OBJ: 4-5.3 Solve multi-step problems. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
25. The table below shows the time in hours an investor spent researching the stock market each week and
the percent gain on investments.
Make a scatter plot and draw a line of fit for the data.
ANS:
Gai
n (
%)
2 4 6 8 10 12 14 16 18 20 x
20
24
28
32
36
40
44
48
52
56
y
Time (h)
A scatter plot is a graph in which two sets of data are plotted as ordered pairs in a coordinate plane.
There is a positive correlation when y increases as x increases. There is a negative correlation when y
decreases as x increases. There is no correlation when x and y are not related.
If the data points do not all lie on a line, but are close to a line, you can draw a line of fit. This line
describes the trend of the data.
PTS: 1 DIF: Advanced REF: Lesson 4-5
OBJ: 4-5.3 Solve multi-step problems. NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Solve multi-step problems. KEY: Multi-step | Problem Solving
26.
Year 2001 2002 2003 2004 2005 2006
Sales ($1,000) 253 242 265 270 269 275
Write an equation of the regression line in the form of . Estimate the sales for 2010.
ANS:
; $298,730
PTS: 1 DIF: Average REF: Lesson 4-6
OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c
TOP: Regression and median fit lines. KEY: linear regression | best-fit line
27.
Game 1 2 3 4 5 6
Score 85 82 83 80 78 75
Write an equation of the best-fit line in the form of . Estimate the score for the 15th game.
ANS:
; 59.1
PTS: 1 DIF: Average REF: Lesson 4-6
OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c
TOP: Regression and median fit lines. KEY: linear regression | best-fit line
28.
Year 1 2 3 4 5 6
Height (ft) 4 10 15 27 51 60
Write an equation of the regression line in the form of . Estimate the height when the tree is
8 years old.
ANS:
; 81.21 feet
PTS: 1 DIF: Average REF: Lesson 4-6
OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c
TOP: Regression and median fit lines. KEY: linear regression | best-fit line
29.
Month 1 2 3 4 5 6
Units Produced 275 400 612 867 1,020 1,465
Write an equation of the best-fit line in the form of . Name the correlation coefficient.
Round to the nearest ten-thousandth.
ANS:
; 0.983
PTS: 1 DIF: Average REF: Lesson 4-6
OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c
TOP: Regression and median fit lines.
KEY: linear regression | best-fit line | correlation coefficient
30.
Place 1 2 3 4 5 6
Score 9.89 9.75 9.72 9.61 9.55 9.42
Write the equation of a median-fit line in the form of . Predict the score of 10th place.
ANS:
; 9.15
PTS: 1 DIF: Average REF: Lesson 4-6
OBJ: 4-6.2 Solve multi-step problems. STA: OK 3.1c
TOP: Regression and median fit lines. KEY: linear regression | median-fit line
Write the function and state the domain and range.
31.
ANS:
domain is all real numbers
range is
PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.
KEY: piecewise-defined function
32.
ANS:
domain is all real numbers
range is all integers
PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.
KEY: greatest integer function
33.
ANS:
domain is all real numbers
range is
PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.
KEY: absolute value function
34.
ANS:
domain is all real numbers
range is all integers
PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.
KEY: greatest integer function
35.
ANS:
domain is all real numbers
range is
PTS: 1 DIF: Average REF: Lesson 4-7
OBJ: 4-7.2 Solve multi-step problems. TOP: Special functions.
KEY: absolute value function
ESSAY
1. Mary charges a flat fee of $5 plus $2 per hour for baby-sitting.
a. Explain how y-intercepts can be used to describe real-world costs.
b. Write a description of a situation in which the y-intercept of its graph is $7.50.
ANS:
Sample answer:
a. The y-intercept is the flat fee in an equation that represents a price.
b. If Mary charges $7.50 as the flat fee plus $2 per hour for babysitting, the graph representing this
situation would have a y-intercept of $7.50.
The linear equation y = mx + b is written in slope-intercept form, where m is the slope and b is the
y-intercept. If a quantity changes at a constant rate over time, it can be modeled by a linear function.
The y-intercept represents a starting point, and the slope represents the rate of change.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-1
OBJ: 4-1.4 Solve problems and show solutions.
NAT: NA 2 | NA 4 | NA 9 | NA 10 | NA 3 | NA 8
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c | OK 2.5a | OK 2.5b
TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
2. A musician’s fan club had 35,000 members in 1999 and grew to 99,000 members by 2004.
Fan club membership
Nu
mb
er o
f m
emb
ers
(in
th
ou
san
ds)
(1999, 35,000)
(2004, 99,000)
1998 1999 2000 2001 2002 2003 2004 x
200
300
400
500
600
700
800
900
1000
1100
y
Year
a. Explain how the slope-intercept form can be used to predict the number of members in 2007.
b. Discuss how slope-intercept form is used in linear extrapolation.
ANS:
Sample answer:
a. You can use the slope-intercept form of the equation to find the y-value for any requested x-value.
The number of members in the fan club in 2007 will be 137,400.
b. Linear extrapolation is when you use a linear equation to predict values that are outside of the given
points on the graph.
Find the slope of the line with the slope formula. Find the y-intercept by replacing x and y with the
given point and m with the slope in the slope-intercept form. Solve for b. Write the equation in
slope-intercept form using the given m and the calculated b.
Linear extrapolation is using a linear equation to predict values that are beyond the range of the data.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-2
OBJ: 4-2.4 Solve problems and show solutions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 3 | NA 4
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.4c
TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
3. Megan wants to change her Internet Service Provider. She is considering three different plans.
Plan 1 charges a $15 monthly fee plus $0.08 per minute of use.
Plan 2 charges a $5 monthly fee plus $0.11 per minute of use.
Plan 3 charges a flat monthly fee of $49.95.
a. For each plan, write an equation that represents the monthly cost C for m minutes per month.
b. Graph each of the three equations on the same coordinate axes. Label each line.
c. Megan expects to use 500 minutes per month. In which plan do you think Megan should enroll?
Explain.
ANS:
Sample Answer
a. Plan 1:
Plan 2:
Plan 3:
b.
Plan1
Plan
2
Plan 3
50 100 150 200 250 300 350 400 450 500 m
5
10
15
20
25
30
35
40
45
50
55
60
C
c. Megan should enroll in Plan 3. The graph shows that at 500 minutes, she would be paying $49.95
for Plan 3, about $60 for Plan 2, and about $55 for Plan 1.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-3
OBJ: 4-3.5 Solve problems and show solutions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c TOP: Performance assessment
KEY: Problem Solving | Show Solutions
4. a. Illustrate how you can determine whether two lines are parallel or perpendicular.
b. Are the two lines graphed below parallel? Explain.
c. Write an equation with a graph perpendicular to the lines graphed. Explain.
O
y x= -(5/8) + (1/8)
y x= -(5/8) + 3
x
y
ANS:
a. Sample answer: If two equations have the same slope, then the lines are parallel. If the product of
their slopes equals –1, then the lines are perpendicular, except for horizontal and vertical lines.
b. Yes, the lines are parallel as the slopes are equal.
c. The graph of is perpendicular to the graph of and because the
slopes are negative reciprocals of each other.
Two nonvertical lines are parallel if they have the same slope.
Two nonvertical lines are perpendicular if the slopes are opposite reciprocals of each other.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-4
OBJ: 4-4.4 Solve problems and show solutions.
NAT: NA 2 | NA 8 | NA 9 | NA 10 | NA 6 | NA 7 | NA 3
STA: OK 1.1 | OK 2.2 | OK 2.3 | OK 2.4b | OK 2.4c | OK 2.4a | OK 2.5a
TOP: Solve problems and show solutions.
KEY: Problem Solving | Show Solutions
5.
Average Hourly Earnings (dollars) of U.S. Production Workers, 1991-2001
Year 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Earnings 10.32 10.57 10.83 11.12 11.43 11.82 12.28 12.78 13.24 13.76 14.32
Source: Bureau of Labor Statistics, U.S. Dept. of Labor
a. Draw a scatter plot with years on the x-axis and earnings on the y-axis.
b. Draw a line of fit for the data.
c. Write the slope-intercept form of an equation for the line of fit.
d. Predict the hourly earnings for production workers in 2005.
ANS:
Sample Answer
a. and b.
Average Hourly Earnings (dollars) of U.S.
Production Workers, 1991-2001
1990 1992 1994 1996 1998 2000 2002 2004 x
10
11
12
13
14
15
16
y
Year
c. Using (1992, 10.57) and (2000, 13.76), the slope of the line is: .
Find b using one of the points.
The equation for the line of fit is
d.
Hourly earnings in 2005 should be about $15.76.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory
*Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-5
OBJ: 4-5.4 Solve problems and show solutions.
NAT: NA 2 | NA 6 | NA 7 | NA 9 | NA 5 | NA 3
STA: OK 2.2 | OK 2.3 | OK 2.4a | OK 2.4b | OK 2.5a | OK 2.1a | OK 2.4e | OK 3.1a
TOP: Performance assessment KEY: Problem Solving | Show Solutions
6. Alan used his graphing calculator to find the best-fit line of a set of data. The correlation coefficient
was -0.965. Explain what that means.
ANS:
The correlation coefficient measures the how closely the best-fit line is modeling the data. The closer it
is to 1 or -1, the more closely it models the data. The best-fit line is a good model for the data because
-0.965 is very close to -1. The fact that it is negative means that there is a negative correlation.
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-6
OBJ: 4-6.3 Solve problems and show solutions. STA: OK 3.1c
TOP: Regression and median fit lines.
KEY: linear regression | best-fit line | correlation coefficient
7. Is a function? Explain.
ANS:
No it is not a function. A function has to have a unique y value for every x value. If x is 2, y would be
either or .
Assessment Rubric
Level 3 Superior *Shows thorough understanding of concepts.
*Uses appropriate strategies.
*Computation is correct.
*Written explanation is exemplary.
*Diagram/table/chart is accurate (as applicable).
*Goes beyond requirements of problem.
Level 2 Satisfactory *Shows understanding of concepts.
*Uses appropriate strategies.
*Computation is mostly correct.
*Written explanation is effective.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies all requirements of problem.
Level 1 Nearly Satisfactory *Shows understanding of most concepts.
*May not use appropriate strategies.
*Computation is mostly correct.
*Written explanation is satisfactory.
*Diagram/table/chart is mostly accurate (as applicable).
*Satisfies most of the requirements of problem.
Level 0 Unsatisfactory *Shows little or no understanding of the concept.
*May not use appropriate strategies.
*Computation is incorrect.
*Written explanation is not satisfactory.
*Diagram/table/chart is not accurate (as applicable).
*Does not satisfy requirements of problem.
PTS: 1 DIF: Advanced REF: Lesson 4-7
OBJ: 4-7.3 Solve problems and show solutions. TOP: Special functions.