Practice and Problem-Solving Exercises

A Practice

See Problem 1.

For each function, determine whether y varies directly with x. If so, find the constant of variation and write the function rule.

7. x	y
   2	14
   3	21
   5	35

8. x	y
   27	9
   30	10
   60	20

9. x	y
   11	22
   16	32
   7	42

10. x	y
    3	9
    4	10
    5	11

See Problem 2.

Determine whether y varies directly with x. If so, find the constant of variation.

11. y = 12 x y equals 12 x
12. y = 6 x y equals 6 x
13. y = − 2 x y equals negative 2 x
14. y = 4 x + 1 y equals 4 x plus 1
15. y = 4 x − 3 y equals 4 x minus 3
16. y = − 5 x y equals negative 5 x
17. y − 6 x = 0 y minus , 6 x equals 0
18. y + 3 = − 3 x y plus 3 equals negative 3 x

See Problem 3.

For Exercises 19–24, y varies directly with x.

19. If y = 4 y equals 4  when x = − 2 , x equals negative 2 comma  find x when y = 6 . y equals 6 .
20. If y = 6 y equals 6  when x = 2 , x equals 2 comma  find x when y = 12 . y equals 12 .
21. If y = 7 y equals 7  when x = 2 , x equals 2 comma  find x when y = 3 . y equals 3 .
22. If y = 5 y equals 5  when x = − 3 , x equals negative 3 comma  find x when y = − 1 . y equals negative 1 .
23. If y = − 7 y equals negative 7  when x = − 3 , x equals negative 3 comma  find y when x = 9 . x equals 9 .
24. If y = 25 y equals 25  when x = 15 , x equals 15 comma  find y when x = 6 . x equals 6 .

    See Problem 4.

25. Distance For a given speed, the distance traveled varies directly with the time. Kate's school is 5 miles away from her home and it takes her 10 minutes to reach the school. If Josh lives 2 miles from school and travels at the same speed as Kate, how long will it take him to reach the school?
26. Conservation A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. How long will it take for the faucet to waste 4 1 2 4 , and 1 half  cups of water?

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