Section 3.4 Slope-Intercept Form of a Linear Equation 241 Concept 4: Writing an Equation of a Line Using Slope-Intercept Form For Exercises 69–80, write an equation of the line given the following information. Write the answer in slopeintercept form if possible. (See Examples 7–8.) 10, 12. 23 69. The slope is , and the y-intercept is (0, 2). 70. The slope is , and the y-intercept is 71. The slope is 10, and the y-intercept is (0,19). 72. The slope is 14, and the y-intercept is (0, 2). 73. The slope is 6, and the line passes through 74. The slope is and the line passes through the point (1,2). the point (4,3). 23 75. The slope is , and the line passes through 76. The slope is , and the line passes through the point (4,5). the point 13, 12. 77. The slope is 0, and the y-intercept is 78. The slope is 0, and the y-intercept is 79. The slope is 5, and the line passes through 80. The slope is and the line passes through the origin. the origin. Expanding Your Skills For Exercises 81–86, write an equation of the line that passes through two points by following these steps: Step 1: Find the slope of the line using the slope formula, m . Step 2: Using the slope from Step 1 and either given point, follow the procedure given in Example 8 to find an equation of the line in slope-intercept form. 81. (2, 1) and (0, 3) 82. (4, 8) and (0, 4) 83. (3, 1) and (3, 3) 84. (2, 3) and (4, 2) 85. (1, 3) and (2, 9) 86. (1, 7) and (2, 4) 87. The number of reported cases of Lyme disease in the United States can be modeled by the equation y 1203x 10,006. In this equation, x represents the number of years since 1993, and y represents the number of cases of Lyme disease. a. What is the slope of this line and what does it mean in the context of this problem? b. What is the y-intercept, and what does it mean in the context of this problem? c. Use the model to estimate the number of cases of Lyme disease in the year 2010. d. During what year would the predicted number of cases be 36,472? 88. A phone bill is determined each month by a $16.95 flat fee plus $0.10/min of long distance.The equation, represents the total monthly cost,C, for x minutes of long distance. a. Identify the slope. Interpret the meaning of the slope in the context of this problem. b. Identify the C-intercept. Interpret the meaning of the C-intercept in the context of this problem. c. Use the equation to determine the total cost of 234 min of long distance. C 0.10x 16.95 y2 y1 x2 x1 3, 6 7 11. . 1 2 4, 13 35,000 30,000 y 5 1203x 1 10,006 25,000 20,000 15,000 Number of Cases of Lyme Disease United States, by Year 10,000 0 0 4 8 12 16 20 Number of Cases Year (x 5 0 represents 1993) 5,000 y x C 50 Phone Bill Cost Versus Number of Minutes of Long Distance C 0.10x 16.95 0 0 50 100 150 200 250 300 Cost ($) Number of Minutes 40 30 20 10 x
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