Section 3.6 Applications of Linear Equations and Modeling 273 For additional exercises, see Classroom Activities 3.6A–3.6C in the Student’s Resource Manual at www.mhhe.com/moh. Section 3.6 Practice Exercises Study Skills Exercise On test day, take a look at any formulas or important points that you had to memorize before you enter the classroom. Then when you sit down to take your test, write these formulas on the test or on scrap paper. This is called a memory dump. Write down the formulas from Chapter 3. Review Exercises 1. Determine the slope of the line defined by 5x 2y 6. 2. Determine the slope of the line defined by m m 2x 8y 15. For Exercises 3–8, find the x- and y-intercepts of the lines, if possible. 1 4 5 2 x-intercept: (6, 0); y-intercept: (0, 5) 1 3, x-intercept: (2, 0); x-intercept: ( 0); y-intercept: (0, ) 14 3. 4. 5. 5x 6y 30 3x 4y 1 y 2x 4 x-intercept: (0, 0); x-intercept: none; y-intercept: (0, 0) y-intercept: (0, 9) 6. 7. 8. y 5x y 9 x 2 Concept 1: Interpreting a Linear Equation in Two Variables 9. The minimum hourly wage, y (in dollars per hour), in the United States can be approximated by the equation y 0.14x 1.60. In this equation, x represents the number of years since 1970 (x 0 represents 1970, x 5 represents 1975, and so on). (See Example 1.) a. Use the equation to approximate the minimum wage in the year 1980. $3.00 b. Use the equation to predict the minimum wage in 2015. $7.90 c. Determine the y-intercept. Interpret the meaning of the y-intercept in the context of this problem. d. Determine the slope. Interpret the meaning of the slope in the context of this problem. The slope is 0.14.This indicates that the 10. The average daily temperature in January for cities along the eastern seaboard of the United States and Canada generally decreases for cities farther north. A city’s latitude in the northern hemisphere is a measure of how far north it is on the globe. The average temperature, y (measured in degrees Fahrenheit), can be described by the equation where x is the latitude of the city. y 2.333x 124.0 a. Use the equation to predict the average daily temperature in January for Philadelphia, Pennsylvania, whose latitude is 40.0°N 30.7° . Round to one decimal place. Federal Minimum Hourly Wage by Year Average Daily Temperature in January along the Eastern Seaboard by Latitude 8 7 6 5 4 2 b. Use the equation to predict the average daily temperature in January for Edmundston, New Brunswick, 47.4°N 13.4° Canada, whose latitude is . Round to one decimal place. c. What is the slope of the line? Interpret the meaning of the slope in terms of latitude and temperature. d. From the equation, determine the value of the x-intercept. Round to one decimal place. Interpret the meaning of the x-intercept in terms of latitude and temperature. y-intercept: (0, 4) x-intercept: (2, 0); y-intercept: none 80 0 0 10 20 30 40 50 Temperature (°F) Latitude 70 60 50 40 30 20 10 y x y 2.333x 124.0 (Source: U.S. National Oceanic and Atmospheric Administration) m 2.333. The average temperature in January decreases at a rate of 2.333° per 1° of latitude. (53.2, 0). At 53.2° latitude, the average temperature in January is 0°. y x 3 0 0 5 10 15 20 25 30 35 40 Minimum Wage ($/hr) Year (x 0 represents the year 1970) 1 y 0.14x 1.60 The y-intercept is (0, 1.6). This indicates that the minimum wage was $1.60 per hour in the year 1970. minimum wage has risen approximately $0.14 per year during this period. Writing Translating Expression Geometry Scientific Calculator Video
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