252 Chapter 3 Graphing Linear Equations in Two Variables a. Use the equation to predict the number of tigers in 1960. b. Use the equation to predict the number of tigers in 2015. c. Determine the slope of the line. Interpret the meaning of the slope in terms of the number of tigers and the year. d. Determine the x-intercept. Interpret the meaning of the x-intercept in terms of the number of tigers. Solution: a. The year 1960 is 60 yr since 1900. Substitute x 60 into the equation. y350x 42,000 y350(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. y350(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. y350x 42,000 0350x 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. Skill Practice 1. 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. a. How much would be charged for a move that required 3 hr? b. How much would be charged for a move that required 8 hr? c. What is the slope of the line and what does it mean in the context of this problem? d. Determine the y-intercept and interpret its meaning in the context of this problem. Answers 1. a. $280 b. $580 c. 60; This means that for each additional hour of service, the cost of the move goes up by $60. d. (0, 100); The $100 charge is a fixed fee in addition to the hourly rate.
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