263 2.5 Equations of Lines and Linear Models Connecting Graphs with Equations The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f. See Example 5. 45. x y –3 –1 3 –3 –1 1 3 0 46. x y –3 –1 3 –1 1 3 0 –3 47. x y –3 –1 3 –3 –1 1 3 0 48. x y –2 2 4 –4 –2 2 0 49. x y –3 –1 1 3 –300 100 300 0 50. x y –10 5 10 –50 50 150 0 Write an equation (a) in standard form and (b) in slope-intercept form for each line described. See Example 6. 51. through 1-1, 42, parallel to x + 3y = 5 52. through 13, -22, parallel to 2x - y = 5 53. through 11, 62, perpendicular to 3x + 5y = 1 54. through 1-2, 02, perpendicular to 8x - 3y = 7 55. through 14, 12, parallel to y = -5 56. through 1-2, -22, parallel to y = 3 57. through 1-5, 62, perpendicular to x = -2 58. through 14, -42, perpendicular to x = 4 Work each problem. 59. Find k so that the line through 14, -12 and 1k, 22 is (a) parallel to 3y + 2x = 6 (b) perpendicular to 2y - 5x = 1. 60. Find r so that the line through 12, 62 and 1-4, r2 is (a) parallel to 2x - 3y = 4 (b) perpendicular to x + 2y = 1. (b) Use the equation from part (a) to estimate average tuition and fees for in-state students at public fouryear colleges in 2016. Round to the nearest dollar. How does the result compare to the actual figure given in the table, $8778? (Modeling) Solve each problem. See Example 7. 61. Annual Tuition and Fees Average annual tuition and fees for in-state students at public four-year colleges are shown in the table for selected years, where x = 0 represents 2013, x = 1 represents 2014, and so on, and y represents the cost in dollars. (a) Use the data points 10, 80702 and 14, 88042 to find a linear equation that models the data. Year Cost (in dollars) 2013 8070 2014 8312 2015 8543 2016 8778 2017 8804 Data from National Center for Education Statistics.
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