Section 3.2 Linear Equations in Two Variables 235 59. 20x 40y 200 60. x 2y 61. x 5y x-intercept: (10, 0); y-intercept: (0, 5) x-intercept: (0, 0); y-intercept: (0, 0) x-intercept: (0, 0); y-intercept: (0, 0) 10 8 y 2 1086 4 2 2 4 6 8 10 4 6 8 10 x 6 4 2 5 4 y 1 54 3 21 1 2 3 4 5 2 3 4 5 x 3 2 1 5 4 y 1 543 21 1 2 3 4 5 2 3 4 5 x 3 2 1 Concept 4: Horizontal and Vertical Lines For Exercises 62–65, answer true or false. If the statement is false, rewrite it to be true. 62. The line defined by x 3 is horizontal. 63. The line defined by y 4 is horizontal. False, x 3 is vertical 64. A line parallel to the y-axis is vertical. 65. A line parallel to the x-axis is horizontal. True True True a. Vertical c. x-intercept: a. Horizontal a. Horizontal (3, 0); no y-intercept c. no x-intercept; y-intercept: (0, 1) c. no x-intercept; y-intercept: (0, 4) 5 4 y 1 543 1 2 3 4 5 21 2 3 4 5 x 3 2 1 x 3 5 4 y 1 543 1 2 3 4 5 21 2 3 4 5 x 3 2 1 y 1 4 y 1 543 2 1 1 2 3 4 5 2 3 4 5 6 x 3 2 1 2y 8 For Exercises 66–74, a. Identify the equation as representing a horizontal or vertical line. b. Graph the line. c. Identify the x- and y-intercepts if they exist. (See Examples 7 and 8.) 66. x 3 67. y 1 68. 2y 8 69. 5x 20 70. x 3 7 71. y 8 13 a. Vertical a. Vertical a. Horizontal c. x-intercept: (4, 0); no y-intercept c. x-intercept: (4, 0); no y-intercept c. no x-intercept; y-intercept (0, 5) 5 4 y 1 2 1 c. All points on the y-axis are y-intercepts; x-intercept: (0, 0) y 1 2 1 c. x-intercept: ( , 0); no y-intercept 32 5 4 y 1 4 3 2 1 1 2 3 4 5 2 3 4 5 6 x 3 2 1 5x 20 43 1 2 3 4 5 2 3 4 5 6 x 3 2 1 x 3 7 54 3 1 2 3 4 5 2 3 4 5 6 7 8 x 2 1 y 8 13 5 4 y 1 2 1 54 3 1 2 3 4 5 2 3 4 5 x 3 2 1 2x 7 10 72. 3y 0 a. Horizontal 73. 5x 0 a. Vertical 74. 2x 7 10 5 4 y 1 543 2 1 1 2 3 4 5 2 3 4 5 x 3 2 1 3y 0 5 4 y 1 2 1 543 1 2 3 4 5 2 3 4 5 x 3 2 1 5x 0 a. Vertical c. All points on the x-axis are x-intercepts; y-intercept: (0, 0) Writing Translating Expression Geometry Scientific Calculator Video
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