C Challenge

47. Writing When you graph an inequality, you can often use the point (0, 0) to test which side of the boundary line to shade. Describe a situation in which you could not use (0, 0) as a test point.

Graphing Calculator Graph each inequality on a graphing calculator. Then sketch the graph.

48. y ≤ | x + 1 | − | x − 1 | y less than or equal to , vertical line x plus 1 vertical line negative vertical line x minus 1 vertical line
49. y > | x | + | x + 3 | y greater than , vertical line x vertical line plus vertical line x plus 3 vertical line
50. y < | x − 3 | − | x + 3 | y less than , vertical line x minus 3 vertical line negative vertical line x plus 3 vertical line
51. y < 7 − | x − 4 | + | x | y less than , 7 minus vertical line x minus 4 vertical line plus vertical line x vertical line

Standardized Test Prep

SAT/ACT

52. Suppose y varies directly with x. If x is 30 when y is 10, what is x when y is 9?
    1. 3
    2. 27
    3. 29
    4. 300 9 300 over 9
53. Which equation represents a line with slope − 2 negative 2  and y-intercept 3?
    6. 3 y = x − 2 3 y equals x minus 2
    7. 3 y = − 2 x + 1 3 y equals negative 2 x plus 1
    8. y = 2 x − 3 y equals 2 x minus 3
    9. y = − 2 x + 3 y equals negative 2 x plus 3
54. What is the vertex of y = | x | − 5 ? y equals vertical line x vertical line negative 5 question mark
    1. (5,0)
    2. ( − 5 , negative 5 comma 0)
    3. (0, 5)
    4. ( 0 , − 5 ) open 0 comma negative 5 close

Extended Response

55. The amount of a commission is directly proportional to the amount of a sale. A realtor received a commission of $48,000 on the sale of an $800,000 house. How much would the commission be on a $650,000 house?

Mixed Review

Graph each function by translating its parent function. See Lesson 2-7.

56. y = | 2 x + 5 | y equals vertical line 2 x plus 5 vertical line
57. y = | x | − 3 y equals vertical line x vertical line negative 3
58. f(x) = | x + 6 |
59. f ( x ) = | x | − 2 f open x close equals vertical line x vertical line negative 2
60. y = | x + 2 | y equals vertical line x plus 2 vertical line
61. y = | x − 1 | + 5 y equals vertical line x minus 1 vertical line plus 5

Determine whether y varies directly with x. If so, find the constant of variation. See Lesson 2-2.

62. y = x + 1 y equals x plus 1
63. y = 100 x y equals 100 x
64. 5 x + y = 0 5 x plus , y equals 0
65. y − 2 = 2 x y minus , 2 equals 2 x
66. x = y 3 x equals , y over 3
67. − 4 = y − x negative 4 equals y minus x
68. y = − 10 x y equals negative 10 x
69. xy = 1

Make a scatter plot and describe the correlation. See Lesson 2-5.

70. {(0, 6), (1, 4), (2, 4), (4, 1), (5, 0)}
71. {( − 10 , 5 ) , negative 10 comma 5 close comma  ( − 5 , − 5 ) , negative 5 comma negative 5 close comma  ( − 2 , 0 ) , negative 2 comma 0 close comma  (0, 3), ( 5 , − 2 ) open 5 comma negative 2 close }

Get Ready! To prepare for Lesson 3-1, do Exercises 72–74.

Graph each equation. Use one coordinate plane for all three graphs. See Lesson 2-3.

72. 3 x − y = 2 3 x minus y equals 2
73. 3 x − y = − 2 3 x minus y equals negative 2
74. x + 3 y = − 2 x plus 3 y equals negative 2

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