282 Chapter 3 Graphing Linear Equations in Two Variables Section 3.6 Applications of Linear Equations and Modeling Key Concepts Linear equations can often be used to describe or model the relationship between variables in a realworld event. In such applications, the slope may be interpreted as a rate of change. Examples Example 1 The number of drug-related arrests for a small city has been growing approximately linearly since 1985. Let y represent the number of drug arrests, and let x represent the number of years after 1985. 4200 Number of Drug Arrests (0, 1890) (20, 3210) 3500 2800 2100 1400 700 y 0 0 5 10 15 20 25 Number of Arrests Year (x 0 represents 1985) x a. Use the ordered pairs (0, 1890) and (20, 3210) to find an equation of the line shown in the graph. m y2 y1 x2 x1 1320 20 66 3210 1890 20 0 The slope is 66, indicating that the number of drug arrests is increasing at a rate of 66 per year. and the y-intercept is (0, 1890). Hence: m 66, y mx b 1 y 66x 1890 b. Use the equation in part (a) to predict the number of drug-related arrests in the year 2015. (The year 2015 is 30 years after 1985. Hence, .) y 661302 1890 y 3870 x 30 The number of drug arrests is predicted to be 3870 by the year 2015.
miller_introductory_algebra_3e_ch1_3
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