See Problem 5.

Make a table of x- and y-values and use it to graph the direct variation equation.

27. x = ( − 1 3 ) y x equals . open , negative , 1 third , close . y
28. y = − 9 x y equals negative 9 x
29. x = y x equals y

B Apply

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

30. x	y
    1	− 2 negative 2
    3	− 8 negative 8
    5	14

31. x	y
    9	6
    12	8
    15	10

32. x	y
    4	1
    6	2
    8	3

33. x	y
    23	24
    55	56
    66	67

34. Think About a Plan Suppose you make a 4-minute local call using a calling card and are charged 7.6 cents. The cost of a local call varies directly with the length of the call. How much more will it cost to make a 30-minute local call?
    • Which quantity is the dependent quantity?
    • How does the word “more” affect the method needed to solve the problem?

Write and graph a direct variation equation that passes through each point.

35. (1, 2)
36. ( − 3 , − 7 negative 3 comma negative 7 )
37. ( 2 , − 9 ) open 2 comma negative 9 close
38. ( − 0.1 , 50 negative 0.1 comma 50 )
39. ( − 5 , − 3 negative 5 comma negative 3 )
40. ( 9 , − 1 ) open 9 comma negative 1 close
41. (7, 2)
42. ( − 3 , 14 ) negative 3 comma 14 close

For Exercises 43–46, y varies directly with x.

43. If y = 1 2 y equals , 1 half  when x = 4 , x equals 4 comma  find y when x = 5 . x equals 5 .
44. If y = 3 4 y equals , 3 fourths  when x = 1 2 , x equals , 1 half , comma  find y when x = 3 . x equals 3 .
45. If y = 5 3 y equals , 5 thirds  when x = 3 4 , x equals , 3 fourths , comma  find x when y = 1 2 . y equals , 1 half , .
46. If y = − 5 8 y equals negative , 5 eighths  when x = 3 2 , x equals , 3 halves , comma  find x when y = 2 5 . y equals , 2 fifths , .

47. Reasoning Explain why you cannot answer the following question.

    If y = 0 y equals 0  when x = 0 , x equals 0 comma  what is x when y = 13 ? y equals 13 question mark

Open-Ended Choose a value of k within the given range. Then write and graph a direct variation function using your value for k.

48. 0 < k < 1 0 less than k less than 1
49. 3 < k < 4.5 3 less than k less than 4.5
50. − 1 < k < − 1 2 negative 1 less than k less than negative , 1 half

51. Error Analysis Identify the error in the statement shown below.

    

52. Sports The number of rotations of a bicycle wheel varies directly with the number of pedal strokes. Suppose that in the bicycle's lowest gear, 6 pedal strokes move the cyclist about 357 in. In the same gear, how many pedal strokes are needed to move 100 ft?
53. Writing Suppose you use the origin to test whether a linear equation is a direct variation function. Does this method work? Support your answer with an example.

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