286 Chapter 3 Graphing Linear Equations in Two Variables Section 3.4 For Exercises 51–56, write each equation in slopeintercept form. Identify the slope and the y-intercept. 51. 52. 5x 2y 10 3x 4y 12 5 2 53. 54. 3 4 ; x 3y 0 5y 8 4 1 3 ; 12 5 m 0; b 55. 56. 2y 5 y x 0 5 2y b For Exercises 57–62, determine whether the equations represent parallel lines, perpendicular lines, or neither. 3 5 l1: y l1: 2x 5y 10 57. 58. l2: y 5 3 x 3 x 1 Neither l2: 5x 2y 20 l1: 3x 2y 6 x 3 59. 60. l1: y 1 4 l2: x 4y 8 l1: 2x 4 x 4 61. 62. l1: y l2: y 2 9 9 2 x 3 l2: y 6 63. Write an equation of the line whose slope is and whose y-intercept is 10, 12. 64. Write an equation of the line that passes through the origin and has a slope of 5. 43 43 65. Write an equation of the line with slope that passes through the point 16, 22. 43 66. Write an equation of the line with slope 5 that passes through the point y 5x 3 5x y 3 or 11, 82. Section 3.5 67. Write a linear equation in two variables in slope-intercept form. (Answers may vary.) 68. Write a linear equation in two variables in standard form. (Answers may vary.) 69. Write the slope formula to find the slope of the 1x1, y12 1x2, y22. line between the points and 70. Write the point-slope formula. y y1 m1x x12 71. Write an equation of a vertical line (answers may vary). For example: x 6 72. Write an equation of a horizontal line (answers may vary). For example: y 5 For Exercises 73–78, write an equation of a line given the following information. 73. The slope is 6 , and the line passes through 11, 82. y 6x 2 6x y 2 the point or 23 74. The slope is , and the line passes through the 18, 22. 2 3 5 3 y or 2x 3y 5 1 4 x 4 y or x 4y 16 18, 52. y 5 y x 6 65 or 6x 5y 30 4x y 31 60 y 56 x 4x y 0. 10, 42 12, 52 x 3. 16, 72 y 4x 31 or Average Height for Girls Based on Age 50 40 0 1 2 3 4 5 6 7 8 9 10 Height (in.) Age (yr) 30 20 10 0 y x y 2.4x 31 point (5, 5). 75. The line passes through the points and 76. The line passes through the points and 77. The line passes through the point (5, 12) and is perpendicular to the line 78. The line passes through the point and is parallel to the line Section 3.6 79. The graph shows the average height for girls based on age. (Source: National Parenting Council) Let x represent a girl’s age, and let y represent her height (in inches). m ; y-intercept: 10, 52 y 5 2 x 5; y 3 4 x 3; m y-intercept: (0, 3) y 1 3 x; m y-intercept: (0, 0) y 12 5 ; y-intercept: a0, y-intercept: a0, 5 2 ; m 0; y x; m 1; y-intercept: (0, 0) y x 6 or 4x 3y 18 Perpendicular y x 1 43 or 4x 3y 3 y 5x or 5x y 0 Perpendicular Parallel Parallel Neither l2: 6x 4y 4 For example: y 3x 2 For example: 5x 2y 4 m y2 y1 x2 x1 a. Use the equation to estimate the average height of a 7-year-old girl. 47.8 in. b. What is the slope of the line? Interpret the meaning of the slope in the context of the problem. The slope is 2.4 and indicates that the average height for girls increases at a rate of 2.4 in. per year. Writing Translating Expression Geometry Scientific Calculator Video
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