Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 1
4.1 Slopes of Lines from Graphs
Answers
1. Find two points on the line. Calculate πππ π
ππ’π.
2. The steepness of the line and whether the line goes up or down from left to right.
3. Positive.
4. From left to right, if the line goes up then the slope is positive, if the line goes down the slope is
negative.
5. 0
6. Undefined
7. 2
8. 1
3
9. 3
4
10. -3
11. β1
4
12. -2
13. -1
14. 3
15. 1
3
16. 3
2
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 2
4.2 Slopes of Lines from Two Points
Answers
1. β2
3
2. 26
5
3. β3
10
4. 1
4
5. β2
5
6. β1
4
7. β12
5
8. undefined
9. β19
23
10.
200 400 600-20
20
40
60
80
100
120
140
160
180
x
y
11. The slope of the line is 1
7, which means that it costs $1 for each additional 7 miles driven.
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 3
12.
-4 -2 2 4 6 8 10 12 14 16 18-750
750
1500
2250
3000
3750
x
y
13. The slope of the line is 180, which means that each additional computer costs $180.
14.
-1 1 2 3 4
-1
1
2
3
4
x
y
15. The slope of the line is 1.3 which means that each additional quart of milk costs $1.30.
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 4
16.
-1 1 2 3 4 5 6 7 8
10
20
30
40
50
60
x
y
17. The slope of the line is 7.5, which means that each additional hour of tutoring costs $7.50.
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 5
4.3 Equations of Lines from Two Points
Answers
1. π¦ = 2π₯ β 5
2. π¦ =1
3π₯ + 6
3. π¦ =3
4π₯ β 8
4. π¦ = β3π₯ + 6
5. π¦ = β1
4π₯ β 1
6. π₯ = β3
7. π¦ = β5
8. π¦ = βπ₯ β 4
9. π¦ =2
5π₯ +
28
5
10. π¦ = β2π₯ + 5
11. π¦ = 6π₯ β 17
12. a) Two points are (320, 124) and (600, 164). The independent variable is the miles traveled and the
dependent variable is the cost.
b) π¦ =1
7π₯ + 78.3.
1
7 means every 7 miles costs $1 and 78.3 is the base cost of having the car for the
month.
13. a) Two points are (10, 1950) and (15, 2850). The independent variable is the computers sold and
the dependent variable is the profit.
b) π¦ = 180π₯ + 150. $180 is the cost per computer and $150 is the base cost before any computers
are sold.
14. a) Two points are (1, 1.65) and (2, 2.95). The independent variable is the number of quarts and the
dependent variable is the cost.
b) π¦ = 1.3π₯ + .35. The 1.3 means each additional quart costs $1.30 and the $0.35 is the base cost
(perhaps for packaging).
15. a) Two points are (3, 25) and (7, 55). The independent variable is the number of hours spent
tutoring and the dependent variable is the money earned.
b) π¦ = 7.5π₯ + 2.5. This means that $7.50 was the money earned per hour and $2.50 was the base
charge for tutoring.
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 6
4.4 Graphs of Lines from Equations
Answers
1. Slope is 5
8 , y-intercept is (0, 3).
2. Slope is β4
5, y-intercept is (0,
3
5).
3. Slope is 4
3, y-intercept is (0, 7).
4. Slope is 0, y-intercept is (0, β7).
5. Slope is 8
9, y-intercept is (0, 3).
6.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
7.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 7
8.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
9.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
10.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 8
11.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
12. Slope is undefined.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
13. Slope is 0.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 9
14. Slope is 0.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
15. Slope is undefined.
-8 -6 -4 -2 2 4 6 8
-8
-6
-4
-2
2
4
6
8
x
y
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 10
4.5 Equations of Lines from Graphs
Answers
1. π¦ = β3π₯ + 5
2. π¦ = 2π₯ β 3
3. π¦ = β4
3π₯ + 5
4. π¦ =5
4π₯ β 3
5. π¦ = β3
2π₯ +
5
2
6. π¦ =1
2π₯ β
1
2
7. π¦ =1
4π₯ +
3
4
8. π¦ = β2
3π₯ +
1
3
9. 5π₯ β π¦ β 4 = 0
10. π₯ + 2π¦ β 4 = 0
11. 5π₯ β 6π¦ β 4 = 0
12. 5π₯ β 6π¦ β 4 = 0
13. You canβt if you cannot easily identify two points on the graph.
14. A vertical line will have the equation π₯ = __ and a horizontal line will have the equation π¦ = ___.
Where the ___ is the x or y intercept.
15. π₯ β 4π¦ β 20 = 0
16. 2π₯ β 3π¦ + 3 = 0
17. 7π₯ β 21π¦ β 9 = 0
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 11
4.6 Equations of Parallel and Perpendicular Lines
Answers
1. Parallel
2. Perpendicular
3. Parallel
4. Neither
5. Perpendicular
6. Parallel
7. π¦ = 5π₯ β 31
8. π¦ =1
4π₯ + 7.25
9. π¦ = β3
2π₯ β 6.5
10. π¦ = β1
2π₯ β 6
11. π¦ = 2π₯
12. π¦ = β1
5π₯ + 4.8
13. π¦ = β5
2π₯ + 4
14. π¦ =1
7π₯ β
11
7
15. π¦ = β7π₯ + 27
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 12
4.7 Applications of Linear Functions
Answers
1. The dependent variable is the profit and the independent variable is the number of candles sold.
2. (4, 30) and (12, 70)
3.
2 4 6 8 10 12 14
10
20
30
40
50
60
70
80
90
Number of Candles Sold
Profit
4. π¦ = 5π₯ + 10
5. The slope is 5. This means each candle sold creates a profit of $5.
6. The profit-intercept is 10. This means each player will have at least a $10 profit even if he/she
doesn't sell any candles.
7. The maximum profit is π¦ = 5(24) + 10 = $130.
8. Domain: {π₯|π₯ β₯ 0, π₯ β π} Range: {π¦|π¦ = 5π₯ + 50, π₯ β π}
9. 16 candles.
10. This data is discrete because you cannot sell portions of candles.
11. The dependent variable is distance from home and the independent variable is time spent driving.
Chapter 4 β Linear Functions Answer Key
CK-12 Algebra I Honors Concepts 13
12. (5, 112) and (7, 15)
13.
1 2 3 4 5 6 7
50
100
150
200
250
300
350
Time Spent Driving (Hours)
Distance from Home (km)
14. π¦ = β48.5π₯ + 354.5
15. The slope is -48.5 which means his speed in kilometers per hour was 48.5.
16. The distance intercept is 354.5 kilometers which means he started 354.5 kilometers from home.
17. It took about 7.3 hours.
18. Domain: {π₯|0 β€ π₯ β€ 7.31, π₯ β π } Range: {π¦|0 β€ π¦ β€ 354.5, π¦ β π }
19. He was 160.5 miles from home
20. 3 hours
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