Section 3.4 Slope-Intercept Form of a Linear Equation 259 Expanding Your Skills For Exercises 85–90, write an equation of the line that passes through two points by following these steps: y2 y1 x2 x1 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. 85. (2, 1) and (0, 3) 86. (4, 8) and (0, 4) 87. (3, 1) and (3, 3) y 2x 3 y x 4 y 1 2 x 4 88. (2, 3) and (4, 2) 89. (1, 3) and (2, 9) 90. (1, 7) and (2, 4) y 4x 1 y x 6 91. 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. 30,457 cases 35,000 30,000 25,000 20,000 15,000 Number of Cases of Lyme Disease United States, by Year 10,000 5,000 y 5 1203x 1 10,006 y 0 0 4 8 12 16 20 Number of Cases Year (x 5 0 represents 1993) d. During what year would the predicted number of cases be 36,472? x 22; the year 2015 92. A phone bill is determined each month by a $16.95 flat fee plus C 0.10x 16.95 $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. The cost is $40.35 Phone Bill Cost Versus Number of Minutes of Long Distance C 0.10x 16.95 C 93. A linear equation is written in standard form if it can be written as Ax By C, where A and B are not both zero. Write the equation in slope-intercept form to show that the slope is given by the ratio, . (B 0.) AB Ax By C A B For Exercises 94–97, use the result of Exercise 93 to find the slope of the line. 94. 2x 5y 8 95. 6x 7y 9 96. 4x 3y 5 97. 11x 8y 4 x m 1203;The slope represents the rate of increase in the number of cases of Lyme disease per year. (0, 10006); In the year 1993 there were 10,006 cases reported. 50 0 0 50 100 150 200 250 300 Cost ($) Number of Minutes 40 30 20 10 x m 0.10. The cost increases by $0.10/min of long distance. (0, 16.95). The monthly bill for 0 min of long distance is $16.95. y 1 3 x 2 the slope is A B y x . C B ; m 6 7 m 2 5 m 11 8 m 4 3 Writing Translating Expression Geometry Scientific Calculator Video
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