56. What is the pitch of a roof that rises vertically 10 in. for each 15 in. it extends horizontally? 57. Determine if the lines are parallel, perpendicular, or neither: y=- 1 7 x + 14 and y = 7x + 7. 58. Determine if the lines are parallel, perpendicular, or neither: y = 5 6 x - 3 and y = 6 5 x + 1 3 . 59. Graph the line that is parallel to y = 2x + 1 and passes through the point (-3, 2). 60. Graph the line that is parallel to y = 2 3 x - 4 and passes through the point (3, 1). 61. Graph the line that is perpendicular to y = -5x + 1 and passes through the point (1, 1). 62. Graph the line that is perpendicular to y = -6x + 5 and passes through the point (-1, 4). 63. Determine if the lines are parallel, perpendicular, or neither: y = 3 and y=- 1 3 . 64. Determine if the lines are parallel, perpendicular, or neither: x = 2 5 and x=- 5 2 . Interpret the meaning of the slope and y-intercept in the context of each situation. 65. Suzy’s car is in the shop, so she is using a rental car. The total cost, in dollars, for Suzy to rent a compact car is given by y = 149x, where x is the number of weeks the car is rented. 66. Mindy has a wedding cake business. Mindy’s total weekly cost, in dollars, for making wedding cakes is given by y = 20x + 50, where x is the number of cakes Mindy makes each week. 67. The average cost, in dollars, of higher education at 4-yr institutions can be approximated by the equation y = 892x + 12,034, where x is the number of years after 1999. (Source: www.infoplease.com) 68. The median annual income, in dollars, for men who complete high school can be modeled by the equation y = 627.5x + 30,818, where x is the number of years after 1996. (Source: www.infoplease.com) 69. The median annual income, in dollars, for women who complete high school can be modeled by the equation y = 641x + 21,506, where x is the number of years after 1996. (Source: www.infoplease.com) 70. The percent of America’s high school seniors who abuse alcohol can be modeled by the equation y = -1.13x + 77.1, where x is the number of years after 2003. You Be the Teacher! Correct each student’s errors, if any. 71. Explain the steps to graph the line that is parallel to 6x - 2y = 4 and passes through the point (1, 2). Sandee’s work: The slope of the line from the given equation is 6. From the point (1, 2), go up 6 units and right 1 unit. 72. Graph the line that is perpendicular to -3x + y = 4 and passes through the point (0, 5). Aisha’s work: x + y = 4 3 - +3 x + 3x y = 3x + 4. So, the slope of the perpendicular line is - 1 3 . The y-intercept of this line is (0, 4). So, to get another point on the graph, I must go down 1 unit and right 3 units. So another point on this line is (3, 3). 6 2 –6 –4 –2 x 2 4 4 –2 y 73. Determine if the lines are parallel, perpendicular, or neither: y = 2x and y=- 1 2 . Warren’s work: perpendicular 74. Determine if the lines are parallel, perpendicular, or neither: x = -2 and y = -2. Crystal’s work: parallel Calculate It! Graph each pair of equations in the ZSquare format on a graphing calculator to determine if the lines are parallel, perpendicular, or neither. 75. y = 5x - 3 and y = 1 5 x + 3 76. y=- 4 3 x + 5 and y = 3 4 x + 1 77. y = 1 6 x + 2 and y=-6x - 4 78. y = 2x + 6 and y = 2x + 3 79. 0.4x + 1.2y = 3.5 and 1.8x - 0.6y = 4.9 80. 5.6x - 3.5y = 8.9 and 2.4x - 1.5y = 2.7 Think About It! Write equations of lines whose graphs are parallel and perpendicular to the graph of the given equation. 81. y = 5x - 3 82. y=- 2 3 x 83. 4x + 3y = 12 84. 7x - 2y = 4 248 Chapter 3 Linear Equations in Two Variables
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