Name ———————————————————————
Date ————————————
Practice B
Lesson
3.6
For use with the lesson “Model Direct Variation”
Tell whether the equation represents direct variation. If so, identify the
constant of variation.
1. y 5 8x
2. y 5 2x 1 1
3. 3x 1 y 5 6
Graph the direct variation equation.
4. y 5 9x
y
9
3
9 x
26
2
6 x
23
21
21
8. 8y 5 x
y
3
y
1
3 x
23
3 x
1
1
21
21
23
1
y
3
1
21
21
3 x
9. 8y 5 6x
3
1
1
23
26
7. 4y 5 212x
3 x
23
21
21
23
23
Lesson 3.6
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
1
22
22
29
y
3
2
23
23
23
y
6
3
29
6. 3y 5 4x
5. y 5 27x
The graph of a direct variation equation is shown. Write the direct
variation equation. Then find the value of y when x 5 10.
y
10.
5
y
11.
(1, 6)
12.
3
5
(22, 5)
(2, 3)
1
3
3
y
3 x
1
21
1
21
3 x
1
y
13.
14.
1
23
21
(24, 22) 23
23
1 x
21
21
3
23
1 x
y
15.
(3, 2)
(21, 5)
5
y
1
21
23
1
3 x
23
21
21
1
x
Algebra 1
Chapter Resource Book
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5/10/11 2:59:43 AM
Name ———————————————————————
Practice B
Lesson
continued
For use with the lesson “Model Direct Variation”
3.6
16.
y
3
(23, 1)
23
Date ————————————
y
17.
18.
3
1
1
23
x
21
21
21
(22, 22)
y
(4, 1)
1
1 x
21
1
3
x
23
23
23
Tell whether the table represents direct variation. If so, write the direct
variation equation.
19.
21.
x
0.5
3
22
1
28
y
9
54
236
18
2144
x
8
2
24
20.5
14
y
7
28
7
2112
4
20.
22.
x
25
3
22
10
20
y
22
1.2
20.8
4
8
x
20.2
22
1
12
18
y
30
3
26
20.5
3
23. x 5 24, y 5 3
24. x 5 216, y 5 24
25. x 5 28, y 5 24
26. x 5 5, y 5 230
1
27. x 5 }, y 5 1
6
28. x 5 8, y 5 23
29. x 5 6, y 5 102
30. x 5 28, y 5 64
31. x 5 15, y 5 9
32. Hooke’s Law The force F required to stretch a spring varies directly with the
amount the spring is stretched s. Eight pounds is needed to stretch a spring
8 inches.
a. Write a direct variation equation that relates F and s.
b. How much force is required to stretch a spring 25 inches?
33. Basement Waterproofing One way to keep moisture out of your basement is to paint
the walls with a waterproof paint. The number g (of gallons) of paint you need varies
directly with the area A of the basement. One gallon of paint covers 100 square feet.
a. Write a direct variation equation that relates g and A.
b. How many gallons do you need to cover 530 square feet?
c. How many square feet does 8.5 gallons of paint cover?
34. Downloading Files The table shows the amount of time t
(in seconds) it takes to download a file of size s (in kilobytes).
a. Explain why s varies directly with t.
b. Write a direct variation equation that relates s and t.
c. How long will it take to download an 800-kilobyte file?
Round your answer to the nearest second.
3-80
Time, t (sec) File size, s (kb)
15
420
30
840
45
1260
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Lesson 3.6
Given that y varies directly with x, use the specified values to write a
direct variation equation that relates x and y.
Algebra 1
Chapter Resource Book
CS10_CC_A1_MECR710723_C3L06PB.indd 80
5/10/11 2:59:44 AM
Lesson 3.6 Model Direct
Variation
29. a. w 5 2.5m b. 12.5 gal
Teaching Guide
Practice B
30. a. C 5 2πr b. 81.64 in.
1. yes; 8 2. no 3. no
y
9
4.
thickness of the spine of one algebra book. So,
the thickness of the stack varies directly with the
number of algebra books used.
y
5.
3
29
2
3
23
23
9 x
26
Practice A
1
6
6.
3
6. yes; }
3
8.
y
3
y
23
1
3 x
23
y
1
21
21
3 x
8.
21
3 x
26
6 x
1
3 x
1
3 x
y
3 x
23
y
15
12.
5
3
2
6 x
1
3 x
y
1
5
15 x
21
23
13. y 5 5x; 50 14. y 5 26x; 260
1
1
15. y 5 2} x; 25 16. y 5 } x; 2
5
2
5
1
17. y 5 2} x; 2} 18. y 5 3x; 30 19. y 5 2x
4
2
1
20. y 5 7x 21. y 5 2} x 22. y 5 210x
4
3
2
1
23. y 5 } x 24. y 5 } x 25. y 5 2} x
10
5
10
1
26. y 5 } x 27. y 5 215x
8
28. a. C 5 0.08n b.
Paper Copier
C
6
5
4
3
2
1
0
9.
y
3
1
3 x
23
21
23
5
10. y 5 6x; 60 11. y 5 2} x; 225
2
3
1
2 20
12. y 5 } x; 15 13. y 5 } x; 5 14. y 5 } x; }
2
2
3
3
10
1
}
}
15. y 5 25x; 250 16. y 5 2 x; 2
3
3
1 5
17. y 5 x; 10 18. y 5 } x; } 19. yes; y 5 18x
4 2
20. yes; y 5 0.4x 21. no 22. no
1
1
1
23. y 5 } x 24. y 5 } x 25. y 5 2} x
7
8
4
3
26. y 5 26x 27. y 5 6x 28. y 5 2} x
8
3
29. y 5 17x 30. y 5 28x 31. y 5 }x
5
32. a. F 5 s b. 25 lb 33. a. g 5 0.01A b. 5.3
gal. c. 850 ft2 34. a. Because the ratios for each
data pair is 28, s varies directly with t. b. s 5 28t
c. about 29 sec
Practice C
8
1. yes; 2 2. no 3. yes; 5 4. yes; }
3
5. no 6. no
7.
3
y
8.
3
1
23
0 10 20 30 40 50 60 70 n
y
1
23
22
22
21
21
23
21
21
26
Cost (dollars)
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
3
1
2
1
23
25
25
1
3
y
10.
1
215
7.
23
1
21
3
11.
y
21
23
23
2
1
7.
9.
22
22
26
1. yes; 2 2. no 3. yes; 21 4. yes; 3 5. no
23
answers
1–5. Answers will depend upon type of ruler
used. 6. The constant of variation is the
21
23
y
1
1
3 x
23
21
21
3 x
23
Number of copies
Algebra 1
Chapter Resource Book
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5/21/11 1:57:14 AM