SECTION 1.5 Lines 45 49. y = 2x (3, 3) L is parallel to y = 2x L x y 3 3 –1 50. y = –x (1, 2) L L is parallel to y = –x x y 3 3 –1 51. y = 2x L is perpendicular to y = 2x (1, 2) L x y 3 3 –1 52. y = –x x y (–1, 1) 1 3 –3 L L is perpendicular to y = –x In Problems 53–78, find an equation for the line with the given properties. Express your answer using either the general form or the slopeintercept form of the equation of a line, whichever you prefer. 53. = Slope 3; containing the point ( ) −2, 3 54. = Slope 2; containing the point ( ) − 4, 3 55. = Slope 1 2 ; containing the point ( ) 3, 1 56. = − Slope 2 3 ; containing the point ( ) − 1, 1 57. Containing the points ( ) 1, 3 and ( ) −1, 2 58. Containing the points ( ) −3, 4 and ( ) 2, 5 59. = − = y Slope 3; -intercept 3 60. = − = − y Slope 2; -intercept 2 61. = − = x y -intercept 4; -intercept 4 62. = = − x y -intercept 2; -intercept 1 63. Slope undefined; containing the point ( ) 2, 4 64. Slope undefined; containing the point ( ) 3, 8 65. Horizontal; containing the point ( ) −3, 2 66. Vertical; containing the point ( ) − 4, 5 67. Parallel to the line = y x2 ; containing the point ( ) −1, 2 68. Parallel to the line = − y x3 ; containing the point ( ) −1, 2 69. Parallel to the line − = − x y2 5; containing the point ( ) 0, 0 70. Parallel to the line − = − x y 2 2; containing the point ( ) 0, 0 71. Parallel to the line = x 5; containing the point ( ) 4, 2 72. Parallel to the line = y 5; containing the point ( ) 4, 2 In Problems 111–114, the equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither. 111. = − = + y x y x 2 3 2 4 112. = − = − + y x y x 1 2 3 2 4 113. = + = − + y x y x 4 5 4 2 114. = − + = − + y x y x 2 3 1 2 2 73. Perpendicular to the line = + y x 1 2 4; containing the point ( ) − 1, 2 74. Perpendicular to the line = − y x2 3; containing the point ( ) − 1, 2 75. Perpendicular to the line − = − x y2 5; containing the point ( ) 0, 4 76. Perpendicular to the line + = x y 2 2; containing the point ( ) −3, 0 79. = + y x2 3 80. = − + y x3 4 81. = − y x 1 2 1 82. + = x y 1 3 2 83. = + y x 1 2 2 84. = + y x2 1 2 85. + = x y2 4 86. − + = x y3 6 87. − = x y 2 3 6 88. + = x y 3 2 6 89. + = x y 1 90. − = x y 2 91. = − x 4 92. = − y 1 93. = y 5 94. = x 2 95. − = y x 0 96. + = x y 0 97. − = y x 2 3 0 98. + = x y 3 2 0 In Problems 99–108, (a) find the intercepts of the graph of each equation and (b) graph the equation. 99. + = x y 2 3 6 100. − = x y 3 2 6 101. − + = x y 4 5 40 102. − = x y 6 4 24 103. + = x y 7 2 21 104. + = x y 5 3 18 105. + = x y 1 2 1 3 1 106. − = x y 2 3 4 107. − = x y 0.2 0.5 1 108. − + = x y 0.3 0.4 1.2 109. Find an equation of the x-axis. 110. Find an equation of the y-axis. In Problems 79–98, find the slope and y-intercept of each line. Graph the line. 77. Perpendicular to the line = x 8; containing the point ( ) 3, 4 78. Perpendicular to the line = y 8; containing the point ( ) 3, 4
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