CHAPTER 6 Linear Equations and Graphing
6.7 Chapter Review
Review Exercises
Plot Points in a Rectangular Coordinate System
In the following exercises, plot each point in a rectangular coordinate system.
1. a) b) c) d) 
2. a) b) c) d) 
3. a) b) c) d) 
4. a) b) c) d) 
Identify Points on a Graph
In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.
5.  6. 
Verify Solutions to an Equation in Two Variables
In the following exercises, which ordered pairs are solutions to the given equations?
7. a) 
8. a) 
Complete a Table of Solutions to a Linear Equation in Two Variables
In the following exercises, complete the table to find solutions to each linear equation.
9.

10. 

11.

12.

Find Solutions to a Linear Equation in Two Variables
In the following exercises, find three solutions to each linear equation.
13.  14. 
15.  16. 
Recognize the Relation Between the Solutions of an Equation and its Graph
In the following exercises, for each ordered pair, decide:
a) Is the ordered pair a solution to the equation?
b) Is the point on the line?
17.
(3, 1) (6, 4) 
18.

Graph a Linear Equation by Plotting Points
In the following exercises, graph by plotting points.
19.  20. 
21.  22. 
23.  24. 
Graph Vertical and Horizontal lines
In the following exercises, graph each equation.
25.  26. 
In the following exercises, graph each pair of equations in the same rectangular coordinate system.
27. and  28. and 
Identify the x– and yIntercepts on a Graph
In the following exercises, find the x– and yintercepts.
29.  30. 
Find the x– and yIntercepts from an Equation of a Line
In the following exercises, find the intercepts of each equation.
31.  32. 
33.  34. 
35.  36. 
Graph a Line Using the Intercepts
In the following exercises, graph using the intercepts.
37.  38. 
39.  40. 
41.  42. 
Use Geoboards to Model Slope
In the following exercises, find the slope modeled on each geoboard.
43.  44. 
45.  46. 
In the following exercises, model each slope. Draw a picture to show your results.
47.  48. 
49.  50. 
In the following exercises, find the slope of each line shown. Use to find the slope of a line from its graph.
51.  52. 
53.  54. 
Find the Slope of Horizontal and Vertical Lines
In the following exercises, find the slope of each line.
55.  56. 
57.  58. 
Use the Slope Formula to find the Slope of a Line between Two Points
In the following exercises, use the slope formula to find the slope of the line between each pair of points.
59.  60. 
61.  62. 
Graph a Line Given a Point and the Slope
In the following exercises, graph each line with the given point and slope.
63. ;  64. ; 
65. yintercept 1;  66. xintercept ; 
Solve Slope Applications
In the following exercises, solve these slope applications.
67. A mountain road rises 50 feet for a 500foot run. What is its slope?  68. The roof pictured below has a rise of 10 feet and a run of 15 feet. What is its slope? 
Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line
In the following exercises, use the graph to find the slope and yintercept of each line. Compare the values to the equation .
69.

70.

Identify the Slope and yIntercept from an Equation of a Line
In the following exercises, identify the slope and yintercept of each line.
71.  72. 
73.  74. 
Graph a Line Using Its Slope and Intercept
In the following exercises, graph the line of each equation using its slope and yintercept.
75.  76. 
77.  78. 
In the following exercises, determine the most convenient method to graph each line.
79.  80. 
81.  82. 
83.  84. 
Graph and Interpret Applications of Slope–Intercept
85. Marjorie teaches piano. The equation models the relation between her weekly profit, P, in dollars and the number of student lessons, s, that she teaches.

86. Katherine is a private chef. The equation models the relation between her weekly cost, C, in dollars and the number of meals, m, that she serves.

Use Slopes to Identify Parallel Lines
In the following exercises, use slopes and yintercepts to determine if the lines are parallel.
87.  88. 
Use Slopes to Identify Perpendicular Lines
In the following exercises, use slopes and yintercepts to determine if the lines are perpendicular.
89.  90. 
Find an Equation of the Line Given the Slope and yIntercept
In the following exercises, find the equation of a line with given slope and yintercept. Write the equation in slope–intercept form.
91. slope and  92. slope and 
93. slope and  94. slope and 
In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.
95.  96. 
97.  98. 
Find an Equation of the Line Given the Slope and a Point
In the following exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.
99. , point  100. , point 
101. , point  102. Horizontal line containing 
Find an Equation of the Line Given Two Points
In the following exercises, find the equation of a line containing the given points. Write the equation in slope–intercept form.
103. and  104. and 
105. and  106. and . 
Find an Equation of a Line Parallel to a Given Line
In the following exercises, find an equation of a line parallel to the given line and contains the given point. Write the equation in slope–intercept form.
107. line , point  108. line , point 
109. line , point  110. line , point 
Find an Equation of a Line Perpendicular to a Given Line
In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope–intercept form.
112. line , point  111. line , point 
114. line point  113. line , point 
Review Answers
1.  3.  
5. a) b) c) d)  7. a, b  
9.

11.


13. Answers will vary.  15. Answers will vary.  
17. a) yes; yes b) yes; no  19.  
21.  23.  
25.  27.  
29.  31.  
33.  35.  
37.  39.  
41.  43.  
45.  47.  
49.  51. 1  
53.  55. undefined  
57. 0  59.  
61.  63.  
65.  67.  
69. slope and yintercept  71.  
73.  75.  
77.  79. horizontal line  
81. intercepts  83. plotting points  
85. a) −?250 b) ?450 c) The slope, 35, means that Marjorie’s weekly profit, P, increases by $35 for each additional student lesson she teaches. The P–intercept means that when the number of lessons is 0, Marjorie loses $250. d) 
87. not parallel  
89. perpendicular  91.  
93.  95.  
97.  99.  
101.  103.  
105.  107.  
109.  111.  
113. 
Practice Test
1. Plot each point in a rectangular coordinate system.
a) 
2. Which of the given ordered pairs are solutions to the equation ? a) 
3. Find three solutions to the linear equation .  4. Find the x– and yintercepts of the equation . 
Find the slope of each line shown.
5.  6. 
7. 
8. Find the slope of the line between the points and .  9. Graph the line with slope containing the point . 
Graph the line for each of the following equations
10.  11. 
12.  13. 
14.  15. 
Find the equation of each line. Write the equation in slope–intercept form.
16. slope and yintercept  17. , point 
18. containing and  19. parallel to the line , containing the point 
20. perpendicular to the line , containing the point 
Practice Test Answers
1.  2. a) yes b) yes c) no 
3. Answer may vary  4. 
5. m =  6. undefined 
7. m = 0  8. 
9. y = x –  10. 
11.  12. 
13.  14. 
15.  16. 
17.  18. 
19.  20. 
Attributions
This chapter has been adapted from “Review Exercises” and “Practice Test” in Chapter 4 of Elementary Algebra (OpenStax) by Lynn Marecek and MaryAnne AnthonySmith, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.