Answer Key – Chapter 8

Exercise 8.1

  1. Solution to Exercise 8.1-1. The graph shows point A (-3, 5) which is 3 units to the left and 5 units up. B (5, -3) is 5 units to the right and 3 units down. C (0, -4) is 4 units down from the origin.
  1. Solution to Exercise 8.1-3. The graph shows point D (-6, 0) which is 6 units to the left. E (-2, 4) is 2 units to the left and 4 units up. F (5, 2) which is 5 units to the right and 2 units up.
  1. a. Quadrant II
    b. Quadrant IV
    c. Quadrant I
  1. a. X-axis (left)
    Quadrant III
    Y-axis (up)
  1. a. 2 units
    Solution to Exercise 8.1-9a. The point (3,4) is 3 units to the right and 4 units up. The point (5,4) is 5 units to the right and 4 units up. The horizontal distance between the 2 points is 2 units.
    b. 9 units
    Solution to Exercise 8.1-9b. The point (-7,1) is 7 units to the left and 1 unit up. The point (2,1) is 2 units to the right and 1 unit up. The horizontal distance between the 2 points is 9 units.
  1. a. 5 units
    Solution to Exercise 8.1-11a.The point (-5,3) is 5 units to the left and 3 units up. The point (0,3) is 3 units up. The horizontal distance between the 2 points is 5 units.
    b. 8 units
    Solution to Exercise 8.1-11b.The point (-2,-2) is 2 units to the left and 2 units down. The point (6,-2) is 6 units to the right and 2 units down. The horizontal distance between the 2 points is 8 units.
  1. a. 5 units
    Solution to Exercise 8.1-13a.The point (3,6) is 3 units to the right and 6 units up. The point (3,1) is 3 units to the right and 1 unit up. The vertical distance between the 2 points is 5 units.
    b. 7 units
    Solution to Exercise 8.1-13b. The point (5,2) is 5 units to the right and 2 units up. The point (5,-5) is 5 units to the right and 5 units down. The vertical distance between the points is 7 units.
  1. a. 4 units
    Solution to Exercise 8.1-15a.The point (5,6) is 5 units to the right and 6 units up. The point (5,2) is 5 units to the right and 2 units up. The vertical distance between the 2 points is 4 units.
    b. 6 units
    Solution to Exercise 8.1-15b. The point (7,2) is 7 units to the right and 2 units up. The point (7,-4) is 7 units to the right and 4 units down. The vertical distance between the 2 points is 6 units.
  1. D (–3, –1)
  1. S(–3, –1)
  1. (1, 12) and (1, –2)
  1. (–7, 3) and (5, 3)

Exercise 8.2

  1. a. 4
    b. 10
    c. 6
    d. 9
    e. 15
    f. 6
  1. a. –3
    b. 3
    c. 1
    d. [latex]\displaystyle{\frac{3}{2}}[/latex]
    e. 6
    f. –6
  1. [latex]5x - 2y = -2[/latex]
  1. [latex]3x + 4y = -12[/latex]
  1. [latex]x - 2y = -3[/latex]
  1. [latex]\displaystyle{y = -\frac{3}{2}x - \frac{3}{4}}[/latex]
  1. [latex]\displaystyle{y = \frac{3}{2}x + 5}[/latex]
  1. [latex]\displaystyle{y = -\frac{3}{2}x + 3}[/latex]
  1. Table of Values for Exercise 17
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]3[/latex] [latex](0, 3)[/latex]
    [latex]1[/latex] [latex]4[/latex] [latex](1, 4)[/latex]
    [latex]2[/latex] [latex]5[/latex] [latex](2, 5)[/latex]
    [latex]3[/latex] [latex]6[/latex] [latex](3, 6)[/latex]

    Solution to Exercise 8.2-17. The solution graph shows the placement of the coordinates for x = 0,1,2,3 from the table of values in the solution.

  1. Table of Values for Exercise 19
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]1[/latex] [latex](0, 1)[/latex]
    [latex]1[/latex] [latex]-4[/latex] [latex](1, -4)[/latex]
    [latex]2[/latex] [latex]-9[/latex] [latex](2, -9)[/latex]
    [latex]3[/latex] [latex]-14[/latex] [latex](3, -14)[/latex]

    Solution to Exercise 8.2-19. The solution graph shows the placement of the coordinates for x = 0,1,2,3 from the table of values in the solution.

  1. Table of Values for Exercise 21
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-1[/latex] [latex](0, -1)[/latex]
    [latex]1[/latex] [latex]-3[/latex] [latex](1, -3)[/latex]
    [latex]2[/latex] [latex]-5[/latex] [latex](2, -5)[/latex]
    [latex]3[/latex] [latex]-7[/latex] [latex](3, -7)[/latex]

    Solution to Exercise 8.2-21. The solution graph shows the placement of the coordinates for x = 0,1,2,3 from the table of values in the solution.

  1. Table of Values for Exercise 23
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-3[/latex] [latex](0, -3)[/latex]
    [latex]1[/latex] [latex]-1[/latex] [latex](1, -1)[/latex]
    [latex]2[/latex] [latex]1[/latex] [latex](2, 1)[/latex]
    [latex]3[/latex] [latex]3[/latex] [latex](3, 3)[/latex]

    Solution to Exercise 8.2-23. The solution graph shows the placement of the coordinates for x = 0,1,2,3 from the table of values in the solution.

  1. x-intercept: [latex]\displaystyle{(-\frac{2}{3}, 0)}[/latex]; y-intercept: [latex]\displaystyle{(0, -2)}[/latex]
    Solution to Exercise 8.2-25. The solution graph shows the placement of the x intercept (-0.67,0) and the y intercept (0,-2).
  1. x-intercept: [latex]7, 0[/latex]; y-intercept: [latex]0, 7[/latex]
    Solution to Exercise 8.2-27. The solution graph shows the placement of the x intercept 7,0) and the y intercept (0,7).
  1. x-intercept: [latex]-2, 0[/latex]; y-intercept: [latex]0, 4[/latex]
    Solution to Exercise 8.2-29. The solution graph shows the placement of the x intercept (-2,0) and the y intercept (0,4).
  1. [latex]\displaystyle{m = \frac{2}{3}; b = -6}[/latex]
    Solution to Exercise 8.2-31. The solution graph shows the placement of the x intercept (9,0) and the y intercept (0,-6).
  1. [latex]\displaystyle{m = \frac{4}{7}; b = 3}[/latex]
    Solution to Exercise 8.2-33. The solution graph shows the placement of the y intercept (0,3). The slope m =4/7 has a rise of 4 and a run of 7.
    1. Positive slope
    1. 0
    1. [latex]\displaystyle{-\frac{5}{8}}[/latex]

8.3 Exercise

    1. [latex]y = 2[/latex]
    1. [latex]y = x - 2[/latex]
    1. [latex]y = -2x + 10[/latex]
    1. [latex]\displaystyle{y = \frac{2}{3}x}[/latex]
    1. [latex]\displaystyle{y = -\frac{3}{2}x + 6}[/latex]
    1. 2
    1. 7
    1. [latex]5x + 3y = 15[/latex]
    1. [latex]2x + y = 1[/latex]

8.4 Exercise

    1. Perpendicular
    1. Parallel
    1. Perpendicular
    1. Neither
    1. [latex]\displaystyle{y = \frac{2}{3}x - \frac{13}{3}}[/latex]
    1. [latex]\displaystyle{y = \frac{1}{3}x - 20}[/latex]
    1. [latex]y = x + 7[/latex]
    1. [latex]\displaystyle{y = -\frac{1}{2}x + 1}[/latex]

Review Exercises 8

  1. a. Quadrant IV
    b. Quadrant II
    c. X-axis (right)
    d. Quadrant IV
    e. X-axis (right)
    f. Y-axis (up)
  1. RectanglePerimeter = 22 units; Area=24 square units
    Solution to Review Exercise 8-3. The graph show points A (6,-3), B (6,-6), C (-2,-6), and D (-2,-3). Points A-D are joined to form a rectangle. The area of the rectangle is 24 units. The area is calculated with the formula (l x w). Length = 8 multiplied by the width = 3. The perimeter of the rectangle is 22 units. The perimeter is calculated with the formula (2l + 2w). Perimeter = 2 multiplied by 8 + 2 multiplied by 3.
  1. Table of Values for Exercise 5
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-2[/latex] [latex](0, -2)[/latex]
    [latex]1[/latex] [latex]2[/latex] [latex](1, 2)[/latex]
    [latex]2[/latex] [latex]6[/latex] [latex](2, 6)[/latex]
    [latex]3[/latex] [latex]10[/latex] [latex](3, 10)[/latex]

    Solution to Review Exercise 8-5. The four points chosen to graph the line include A (0,-2), B (1,2), C (2,6), and D(3,10) as shown in the solution table.

  1. Table of Values for Exercise 7
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]4[/latex] [latex](0, 4)[/latex]
    [latex]1[/latex] [latex]3[/latex] [latex](1, 3)[/latex]
    [latex]2[/latex] [latex]2[/latex] [latex](2, 2)[/latex]
    [latex]3[/latex] [latex]1[/latex] [latex](3, 1)[/latex]

    Solution to Review Exercise 8-7. The four points chosen to graph the line include A (0,4), B (1,3), C (2,2), and D(3,1) as shown in the solution table.

  1. Table of Values for Exercise 9
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]2[/latex] [latex](0, 2)[/latex]
    [latex]2[/latex] [latex]3[/latex] [latex](2, 3)[/latex]
    [latex]4[/latex] [latex]4[/latex] [latex](4, 4)[/latex]
    [latex]6[/latex] [latex]5[/latex] [latex](6, 5)[/latex]

    Solution to Review Exercise 8-9. The four points chosen to graph the line include A (0,2), B (2,3), C (4,4), and D (6,5) as shown in the solution table.

  1. Table of Values for Exercise 11
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-3[/latex] [latex](0, -3)[/latex]
    [latex]4[/latex] [latex]0[/latex] [latex](4, 0)[/latex]
    [latex]8[/latex] [latex]3[/latex] [latex](8, 3)[/latex]

    Solution to Review Exercise 8-11. The y-intercept is (0,-3), the x-intercept is (4,0) and the 3rd point is (8,3) as shown in the solution table.

  1. Table of Values for Exercise 13
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-3[/latex] [latex](0, -3)[/latex]
    [latex]6[/latex] [latex]0[/latex] [latex](6, 0)[/latex]
    [latex]2[/latex] [latex]-2[/latex] [latex](2, -2)[/latex]

    Solution to Review Exercise 8-13.The y-intercept is (0,-3), the x-intercept is (6,0) and the 3rd point is (2,-2) as shown in the solution table.

  1. Table of Values for Exercise 15
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]0[/latex] [latex](0, 0)[/latex]
    [latex]1[/latex] [latex]4[/latex] [latex](1, 4)[/latex]

  1. [latex]m = 4; b = 6[/latex]
    Solution to Review Exercise 8-17. The y-intercept is (0,6). Using the slope, y-intercept method [latex]m = 4; b = 6[/latex], from the y-intercept move up 4 units and to the right 1 unit to get the next point.
  1. [latex]\displaystyle{m = -\frac{3}{2}; b = 6}[/latex]
    Solution to Review Exercise 8-19. The y-intercept is (0,6). Using the slope, y-intercept method [latex]\displaystyle{m = -\frac{3}{2}; b = 6}[/latex], from the y-intercept move up 3 units and to the right 2 units to get the next point.
  1. [latex]\displaystyle{m = -\frac{3}{4}; b = -1}[/latex]
    Solution to Review Exercise 8-21. The y-intercept is (0,-1). Using the slope, y-intercept method [latex]\displaystyle{m = -\frac{3}{4}; b = -1}[/latex], from the y-intercept move down 3 units and to the right 4 units to get the next point.
  1. [latex]\displaystyle{y = \frac{3}{4}x - \frac{1}{4}}[/latex]
  1. [latex]\displaystyle{y = -\frac{4}{3}x + \frac{8}{3}}[/latex]
  1. [latex]y = 3x - 5[/latex]
  1. [latex]\displaystyle{y = \frac{3}{4}x + \frac{9}{2}}[/latex]
  1. [latex]y = -2x + 1[/latex]

Self-Test Exercises 8

  1.     [latex](-3, -1)[/latex]; Area = 40 square units
    1. [latex]2x - 3y = 6[/latex]
    2. [latex]\displaystyle{x = \frac{25}{8}}[/latex]
    1. [latex]\displaystyle{y = \frac{2}{3}x = 2}[/latex]
    2. [latex]\displaystyle{y = -\frac{3}{4}x + \frac{5}{4}}[/latex]
  4. Table of Values for Self-Test Exercise 4
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]-3[/latex] [latex](0, -3)[/latex]
    [latex]3[/latex] [latex]-1[/latex] [latex](3, -1)[/latex]
    [latex]6[/latex] [latex]1[/latex] [latex](6, 1)[/latex]
    [latex]9[/latex] [latex]3[/latex] [latex](9, 3)[/latex]

    The line on the graph shows points (0,-3), (3,-1), (6,1), and (9,3) as shown in the previous table of values.

  5. Table of Values for Self-Test Exercise 5
    [latex]x[/latex] [latex]y[/latex] [latex](x, y)[/latex]
    [latex]0[/latex] [latex]0[/latex] [latex](0, 0)[/latex]
    [latex]3[/latex] [latex]-4[/latex] [latex](3, -4)[/latex]
    [latex]6[/latex] [latex]1[/latex] [latex](6, 1)[/latex]

The line on the graph shows points (0,0), and (3,-4) as shown in the previous table of values.

6. a)
The y-intercept (0,-4) is shown and the slope is used to find the next point. From the y-intercept move down 1 unit and to the right 2 units.

b)
The y-intercept (0,-2) is shown and the slope is used to find the next point. From the y-intercept move up 2 units and to the right 3 units.

  1. [latex]4x + 5y = 9[/latex]
  1. [latex]3x - 5y = 15[/latex]
  1. [latex]3x - 2y = -12[/latex]
  1. [latex]\frac{4}{3}x - y = 0[/latex]

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