43. Think About a Plan What point(s) do the graphs of y = | x − 2 | y equals vertical line x minus 2 vertical line  and y = | x + 4 | y equals vertical line x plus 4 vertical line  have in common?

    • How are these graphs related?
    • Could a graph or a table help you solve this problem?
44. What point(s) do the graphs of y = − | x | + 7 y equals negative vertical line x vertical line plus 7  and y = | x − 3 | y equals vertical line x minus 3 vertical line  have in common?

Graph each translation of y = | x | . bold italic y equals vertical line bold italic x vertical line .  Describe how the graph is related to the graph of y = | x | . bold italic y equals vertical line bold italic x vertical line .

45. y = | x − 1 | + 2 y equals vertical line x minus 1 vertical line plus 2
46. y = | x + 2 | − 1 y equals vertical line x plus 2 vertical line negative 1
47. 1. Graph y = | x − 2 | + 3 . y equals vertical line x minus 2 vertical line plus 3 .
    2. The vertex of an absolute value function is the point at which its graph changes direction. What is the vertex of the graph of y = | x − 2 | + 3 ? y equals vertical line x minus 2 vertical line plus 3 question mark
    3. Reasoning What relationship do you see between the vertex and the equation? What is the vertex of the graph of y = | x − h | + k ? y equals vertical line x minus h vertical line plus k question mark

C Challenge

48. 1. Graph y = | 2 x | y equals vertical line 2 x vertical line  by making a table of values.
    2. Translate y = | 2 x | y equals vertical line 2 x vertical line  to graph y = | 2 x | + 3 . y equals vertical line 2 x vertical line plus 3 .
    3. Translate y = | 2 x | y equals vertical line 2 x vertical line  to graph y = | 2 ( x − 1 ) | . y equals vertical line 2 open x minus 1 close vertical line .
    4. Translate y = | 2 x | y equals vertical line 2 x vertical line  to graph y = | 2 ( x − 1 ) | + 3 . y equals vertical line 2 open x minus 1 close vertical line plus 3 .
49. Graph y = − | x + 4 | − 7 . y equals negative vertical line x plus 4 vertical line negative 7 .

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

50. For f ( x ) = 5 x − 7 , f open x close equals 5 x minus 7 comma  what value of x gives f ( x ) = − 3 ? f open x close equals negative 3 question mark

51. What is the slope of the line below?

    

52. What is the value of f ( x ) = x 2 − 4 x + 6 f open x close equals , x squared , minus 4 x plus 6  when x = − 3 ? x equals negative 3 question mark
53. What is the x-intercept of the line y = − 4 x + 2 ? y equals negative 4 x plus 2 question mark

Mixed Review

See Lesson 5-7.

The data below follow a linear model. Write an equation of a trend line or use a graphing calculator to find an equation of the line of best fit.

54. Year	1	2	3	4
    Price	$5.30	$5.57	$5.82	$6.05

55. Ounces	8	12	16	20
    Calories	100	151	202	250

Get Ready! To prepare for Lesson 6-1, do Exercises 56–59.

See Lesson 5-3.

Graph each equation.

56. y = 2 x − 1 y equals 2 x minus 1
57. y = − 3 x + 5 y equals negative 3 x plus 5
58. y = 1 3 x + 2 y equals , 1 third , x plus 2
59. y = − 5 2 x − 7 y equals negative , 5 halves , x minus 7

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