Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Determine whether each equation represents a direct variation. If it does, find the constant of variation.

9. 2 y = 5 x + 1 2 y equals 5 x plus 1
10. 8 x + 9 y = 10 8 x plus 9 y equals 10
11. − 12 x = 6 y negative 12 x equals 6 y
12. y + 8 = − x y plus 8 equals negative x
13. − 4 + 7 x + 4 = 3 y negative 4 plus 7 x plus 4 equals 3 y
14. 0.7 x − 1.4 y = 0 0.7 x minus 1.4 y equals 0

Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 12 . bold italic x equals 12 .  See Problem 2.

15. y = − 10  when  x = 2 . y equals negative 10 , when , x equals 2 .
16. y = 7 1 2  when  x = 3 . y equals , 7 , and 1 half . when , x equals 3 .
17. y = 5  when  x = 2 . y equals 5 , when , x equals 2 .
18. y = 125  when  x = − 5 . y equals 125 , when , x equals negative 5 .
19. y = 10.4  when  x = 4 . y equals , 10.4 . when , x equals 4 .
20. y = 9 1 3  when  x = − 1 2 . y equals , 9 , and 1 third . when , x equals negative , 1 half , .

See Problem 3.

Graph each direct variation equation.

21. y = 2 x y equals 2 x
22. y = 1 3 x y equals , 1 third , x
23. y = − x y equals negative x
24. y = − 1 2 x y equals negative , 1 half , x
25. Travel Time The distance d you bike varies directly with the amount of time t you bike. Suppose you bike 13.2 mi in 1.25 h. What is an equation that relates d and t? What is the graph of the equation?
26. Geometry The perimeter p of a regular hexagon varies directly with the length l of one side of the hexagon. What is an equation that relates p and l? What is the graph of the equation?

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