Section 3.6 Applications of Linear Equations and Modeling 253 2. Writing a Linear Model Using Observed Data Points Writing a Linear Model from Observed Data Points Example 2 The monthly sales of hybrid cars sold in the United States are given for a recent year. The sales for the first 8 months of the year are shown in Figure 3-35. The value x 0 represents January, x 1 represents February, and so on. y x 30,000 25,000 20,000 15,000 Monthly Hybrid Vehicle Sales in the United States 10,000 (5, 23,400) 00 1 2 3 4 5 6 Number of Vehicles Sold Month (x 0 represents January) 5,000 7 (0, 14,400) Figure 3-35 a. 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, 14,400) and (5, 23,400) are given in the graph. Use these points to find the slope. (0, 14,400) and (5, 23,400) (x1, y1) (x2, y2) Label the points. 23,400 14,400 9000 5 1800 m y2 y1 x2 x1 5 0 The slope is 1800.This indicates that sales increased by approximately 1800 per month during this time period. With m 1800, and the y-intercept given as (0, 14,400), we have the following linear equation in slope-intercept form. y 1800x 14,400 b. To approximate the sales in month number 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.
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