Post on 04-Jan-2016
Pg. 239-242 #4-18 e, 22-28e, 36-42e, 43
Wir2.5• LESSON
Prior Knowledge AssessmentSlope Inside-Outside Activity
Remember:
Directions:- get a white board, marker & eraser
- find a partner- do your own problem on ½ of your white board
- do your partner’s problem on the other ½ of board- check each other’s work
-
4-5 Graphs Using Slope-Intercept Form
Copy and complete the table. Then write a generalization about the meaning of m and b in y=mx+b.
Equation Two Solutions Slope Y-intercept
1. y=2x+1 (0,___) (___,0)
2. y=-2x-3 (0,___) (___,0)
3. y=x+4 (0,___) (___,0)
4. y=0.5x-2.5 (0,___) (___,0)
1 -1/2
-3 -3/2
4 -4
-2.5 5
𝟐𝟏 1
−𝟐𝟏𝟏𝟏𝟏𝟐
-3
4
-2.5
Slope-Intercept Form of the Equation of a Line:
y = mx+b
- m = slope
- m =
- parallel lines
have same slope
- b = y-intercept
- where the graph crosses the y-axis
2 1
2 1
r y yise
ru x xn
Slope-Intercept Form
Slope-Intercept:
Rap
Dance
Animated Activity:
Slope-Intercept Form
Notebook File:
Exploring Slope-Intercept Form
EXAMPLE 1 Identify slope and y-intercept
Identify the slope and y-intercept of the line with the given equation.
y = 3x + 41. 3x + y = 22.
SOLUTION
The equation is in the form y = mx + b. So, the slope of the line is 3, and the y-intercept is 4.
a.
b. Rewrite the equation in slope-intercept form by solving for y. 3x + y = 2 Write original equation.
y = –3x + 2Subtract 3x from each side.
ANSWER
The line has a slope of –3 and a y-intercept of 2.
-3x -3x
Guided Practice – for Example 1
1.) y=-x+2
x+32.) y=
23.) y=-4
4.) 2x-4y=16
5.) 12x+4y-2=0
Write the equations in slope-intercept form and name the slope and y-intercept.
3.) y=-4 m=0 (for horizontal lines) b=
1 3 1 32.) y=
1 14.) y=-
x-4
1.) y=(-
m=
1)x+2 m=-1
- b=-4
:
1 15.) y
b
=-
=
3x+ m=-3
m= b=2 2
-
2 2
b=2 2
2
2 24
Answers
x
EXAMPLE 2 Graph an equation using slope-intercept form
Graph the equation 2x + y = 3.
SOLUTION STEP 1
Rewrite the equation in slope-intercept form. y –2x + 3=
Identify the slope and the y-intercept.STEP 2= –2m and = 3b
STEP 3 Plot the point that corresponds to y-intercept, (0, 3).
STEP 4 Use the slope to locate a second point on the line. Draw a line through the two points.
ESCALATORS
EXAMPLE 3 Change slopes of lines
To get from one floor to another at a library, you can take either the stairs or the escalator. You can climb stairs at a rate of 1.75 feet per second, and the escalator rises at a rate of 2 feet per second. You have to travel a vertical distance of 28 feet. The equations model the vertical distance d (in feet) you have left to travel after t seconds.
Stairs: d = –1.75t + 28 Escalator: d = –2t + 28
a. Graph the equations in the same coordinate plane.
b. How much time do you save by taking the escalator?
EXAMPLE 3 Change slopes of lines
SOLUTION
a. Draw the graph of d = –1.75t + 28 using the fact that the d-intercept is 28 and the slope is –1.75. Similarly, draw the graph of d = –2t + 28. The graphs make sense only in the first quadrant.
The equation d = –1.75t + 28 has a t-intercept of 16. The equation d = –2t + 28 has a t-intercept of 14. So, you save 16 – 14 = 2 seconds by taking the escalator.
b.
Guided Practice – for Examples 2 & 3Graph the equation using slope-intercept form.
2y=
3
6.)
7.)
8.)
9.) x+y=0
10.)
y
2x+3y-4=x+5
=2x
y=-x
+4
-1
x
2m= 0 6.) 7.) 8.)
9.) y=-x m=-1 b=0 1 1
y=-
Answers:
x+3
m=2
m=
m=-1
- b=33 3
10.) 11.)
b=4
sav
b
es
=-
c
31
6 se .
b
WHAT IF? In Example 3, suppose a person can climb stairs at a rate of 1.4 feet second. How much time does taking the escalator save?
11.)
EXAMPLE 4 Change intercepts of lines
TELEVISION
A company produced two 30 second commercials, one for $300,000 and the second for $400,000. Each airing of either commercial on a particular station costs $150,000. The cost C (in thousands of dollars) to produce the first commercial and air it n times is given by C = 150n + 300. The cost to produce the second and air it n times is given by C = 150n + 400.
a.
Graph both equations in the same coordinate plane.
b. Based on the graphs, what is the difference of the costs to produce each commercial and air it 2 times? 4 times? What do you notice about the differences of the costs?
EXAMPLE 4 Change intercepts of lines
SOLUTION
a.
The graphs of the equations are shown.
b. You can see that the vertical distance between the lines is $100,000 when n = 2 and n = 4.
The difference of the costs is $100,000 no matter how many times the commercials are aired.
EXAMPLE 5 Identify parallel lines
Determine which of the lines areparallel.
Find the slope of each line.
Line a: m = –1 – 0–1 – 2
–3 – (–1 )0 – 5
=–1–3
13=
Line b: m = –2–5= 2
5=
Line c: m = –5 – (–3)
–2 – 4–2–6=
1 3=
ANSWER
Line a and line c have the same slope, so they are parallel.
EXAMPLE 5 Identify parallel linesGUIDED PRACTICE for Examples 4 and 5
WHAT IF? In Example 4, suppose that the cost of producing and airing a third commercial is given by C = 150n + 200. Graph the equation. Find the difference of the costs of the second commercial and the third.
12.)
ANSWER 200,000
Determine which lines are parallel: line a through (1, 2) and (3, 4); line b through (3, 4) and (5, 8); line c through (9, 2) and (1, 2).
13.)
ANSWER a and c
Slope-Intercept Games
Algebra vs. The Cockroaches
Planet Hop
Summary• Why is the equation y=mx+b called slope-intercept
form?• Ans: slope (m) and y-intercept (b) are easy to read
from the equation• Explain how to graph 2x-3y=6 using slope-intercept
form?• Ans: solve for y in terms of x first, then graph the y-
intercept and use the slope to find two more points, connect all three points to draw the line
• Decide whether the graphs of y=x+2 and y=x-4 are parallel lines.
• Ans: both have the same slope, so they ARE parallel
NAME
Check Yourself
Pg. 247-250 # 4-16eoe, 17-20,24-38e, 46-47