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?
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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.
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9.
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10. |
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11.
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12.
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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.
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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 y-Intercepts on a Graph
In the following exercises, find the x– and y-intercepts.
| 29. | 30. |
Find the x– and y-Intercepts 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. y-intercept 1; | 66. x-intercept ; |
Solve Slope Applications
In the following exercises, solve these slope applications.
| 67. A mountain road rises 50 feet for a 500-foot 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 y-intercept of each line. Compare the values to the equation .
| 69.
|
70.
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Identify the Slope and y-Intercept from an Equation of a Line
In the following exercises, identify the slope and y-intercept 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 y-intercept.
| 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
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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.
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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.
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Use Slopes to Identify Parallel Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are parallel.
| 87. | 88. |
Use Slopes to Identify Perpendicular Lines
In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.
| 89. | 90. |
Find an Equation of the Line Given the Slope and y-Intercept
In the following exercises, find the equation of a line with given slope and y-intercept. 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.
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11.
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| 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 y-intercept | 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 y-intercepts 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 y-intercept | 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 Anthony-Smith, which is under a CC BY 4.0 Licence. Adapted by Izabela Mazur. See the Copyright page for more information.