2.3 Direct Variation
Name:
For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation.
28.
29.
30.
31.
Write an equation for a direct variation with a graph that passes through each point.
33. (1,2)
34. (3,7)
35. (2,9)
36. (0.1,50)
37. (5,3)
38. (9,1)
39. (7,2)
40. (3,14)
In Exercises 41-45, y varies directly with x.
41. If y  7 when x  3 , find x when y  21 .
42. If y  25 when x  15 , find x when y  10 .
43. If y  30 when x  3 , find y when x  9 .
44. If y  20 when x  2 , find y when x  14 .
45. If y  0.9 when x  4.8 , find y when x  6.4 .
Determine whether a line with the given slope through the given point represents a direct variation. Explain.
46. m  1.7, (9,9) .
5
6
1
2
47. m   , (15,12 )
48. m 
7
1
3
, (6 ,22 )
2
2
4
52. Suppose you drive a car 392 mi on one tank of gas. The tank holds 14 gallons. The number of miles traveled varies
directly with the number of gallons of gas use.
a. Write an equation that relates miles traveled to gallons of gas used.
b. You only have enough money to buy 3.7 gallons of gas. How far can you drive before refueling?
c. Last year you drove 11,700 mi. About how many gallons of gas did you use?
d. Suppose the price of gas averaged $1.57 per gallon last year. Find the cost per mile.
In Exercises 55-58, y varies directly with x.
55. If x is doubled, what happens to y?
56. If x is halved, what happens to y?
57. If x is divided by 7, what happens to y?
58. If x is multiplied by 10, what happens to y?
59. If z varies directly with the product of x and y (z = kxy), then z is said to vary jointly with x and y.
a. The area of a triangle varies jointly with its base and height. What is the constant of variation?
b. Suppose q varies jointly with v and s, and q = 24 when v = 2 and s = 3. Find q when v = 4 and s = 2.
c. Suppose z varies jointly with x and y, and x varies directly with w. Show that z varies jointly with w and y.