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270 Chapter 3 Graphing Linear Equations in Two Variables Solution: a. The year 1960 is 60 yr since 1900. Substitute x 60 into the equation. y 350x 42,000 y 350(60) 42,000 21,000 There were approximately 21,000 tigers in India in 1960. b. The year 2015 is 115 yr since 1900. Substitute x 115. y 350(115) 42,000 1750 There will be approximately 1750 tigers in India in 2015. c. The slope is 350. The slope means that the tiger population is decreasing by 350 tigers per year. d. To find the x-intercept, substitute y 0. y 350x 42,000 0 350x 42,000 Substitute 0 for y. 42,000 350x 120 x The x-intercept is (120, 0). This means that 120 yr after the year 1900, the tiger population would be expected to reach zero.That is, in the year 2020, there will be no tigers left in India if this linear trend continues. 2. Writing a Linear Model Using Observed Data Points Writing a Linear Model from Observed Data Points 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. Monthly Hybrid Vehicle Sales in the United States Figure 3-35 y x 30,000 25,000 20,000 15,000 10,000 (5, 23400) 00 1 2 3 4 5 6 Number of Vehicles Sold Month (x 0 represents January) 5,000 7 (0, 14400) Example 2 Skill Practice The cost y (in dollars) for a local move by a small moving company is given by y 60x 100, where x is the number of hours required for the move. 1. How much would be charged for a move that required 3 hr? 2. How much would be charged for a move that required 8 hr? 3. What is the slope of the line and what does it mean in the context of this problem? 4. Determine the y-intercept and interpret its meaning in the context of this problem. Classroom Example: p. 273, Exercise 10 Skill Practice Soft drink sales at a concession stand at a softball stadium have increased linearly over the course of the summer softball season. 160 Soft Drinks Sold (7, 155) (1, 65) 140 120 100 80 60 40 20 y 0 0 1 2 3 4 5 6 7 8 Number Sold Week Number 5. Use the given data points to find a linear equation that relates the sales, y, to week number, x. 6. Use the equation to predict x the number of soft drinks sold in week 10. Classroom Example: p. 276, Exercise 18 Answers 1. $280 2. $580 3. 60; This means that for each additional hour of service, the cost of the move goes up by $60. 4. (0, 100); The $100 charge is a fixed fee in addition to the hourly rate. 5. y 15x 50 6. 200 soft drinks


miller_introductory_algebra_3e_ch1_3
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