Section 3.6 Applications of Linear Equations and Modeling 269 Expanding Your Skills For Exercises 61–64, write an equation in slope-intercept form for the line shown. 5 y 1 21 5 y 1 21 5 y 1 21 5 y 1 21 Applications of Linear Equations and Modeling Section 3.6 1. Interpreting a Linear Equation in Two Variables Linear equations can often be used to describe (or model) the relationship between two variables in a real-world event. Interpreting a Linear Equation Example 1 Since the year 1900, the tiger population in India has continually decreased. A recent study showed this decrease can be approximated by the equation y350x 42,000.The variable y represents the number of tigers left in India, and x represents the number of years since 1900. 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. y 45,000 40,000 35,000 30,000 25,000 20,000 Number of Tigers in India by Year 10,000 Interpret the meaning of the x-intercept in terms of the number of tigers. x 15,000 0 0 15 30 45 60 75 90 105 120 Number of Tigers Year (x 0 represents the year 1900) 5,000 y 350x 42,000 61. 62. 63. 64. 1 2 3 4 5 22 23 24 25 x 4 3 2 1 2 3 4 5 2524 232221 22 23 24 25 x 4 3 2 2524 232221 1 2 3 4 5 22 23 24 25 x 4 3 2 1 2 3 4 5 2524 232221 22 23 24 25 x 4 3 2 2524 232221 y 2x 4 y 3x 3 y 1 2 x 1 y x 4 Concepts 1. Interpreting a Linear Equation in Two Variables 2. Writing a Linear Model Using Observed Data Points 3. Writing a Linear Model Given a Fixed Value and a Rate of Change Writing Translating Expression Geometry Scientific Calculator Video
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