a. Section 3.6 Applications of Linear Equations and Modeling 271 Use the data points from Figure 3-35 to find a linear equation that represents the monthly sales of hybrid cars in the United States. Let x represent the month number and let y represent the number of vehicles sold. b. Use the linear equation in part (a) to estimate the number of hybrid vehicles sold in month 7 (August). Solution: a. The ordered pairs (0, 14400) and (5, 23400) are given in the graph. Use these points to find the slope. (0, 14400) and (5, 23400) (x1, y1) (x2, y2) Label the points. 23,400 14,400 9000 5 1800 m y2 y1 x2 x1 5 0 With m 1800, and the y-intercept given as (0, 14400), we have the following linear equation in slope-intercept form. y 1800x 14,400 b. To approximate the sales in month 7, substitute x 7 into the equation from part (a). y 1800(7) 14,400 Substitute x = 7. 27,000 The monthly sales for August (month 7) would be 27,000 vehicles. 3. Writing a Linear Model Given a Fixed Value and a Rate of Change Another way to look at the equation is to identify the term mx as the variable term and the term b as the constant term. The value of the term mx will change with the value of x (this is why the slope, m, is called a rate of change). However, the term b will remain constant regardless of the value of x.With these ideas in mind, we can write a linear equation if the rate of change and the constant are known. y mx b Writing a Linear Model Example 3 A stack of posters to advertise a production by the theater department costs $19.95 plus $1.50 per poster at the printer. a. Write a linear equation to compute the cost, c, of buying x posters. b. Use the equation to compute the cost of 125 posters. Skill Practice The monthly cost for a “minimum use” cellular phone is $19.95 plus $0.10 per minute for all calls. 7. Write a linear equation to compute the cost, c, of using t minutes. 8. Use the equation to determine the cost of using 150 minutes. Answers 7. c 0.10t 19.95 8. $34.95 The slope is 1800.This indicates that sales increased by approximately 1800 per month during this time period. Classroom Example: p. 276, Exercise 20
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