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258 Chapter 3 Linear Equations in Two Variables 5b. The average price of a movie ticket in 1996 was $4.42. The average price of a movie ticket in 2010 was $7.89. (Source: http://www.natoonline.org/statisticstickets.htm) i. Write a linear equation that represents the average price of a movie ticket, where x is the years after 1996. ii. Use the equation to predict the average price of a movie ticket in 2015. iii. In what year will the average price of a movie ticket be $10.67? Solution 5b. In this problem, x represents the years after 1996 and y represents the average price of a movie ticket. The year 1996 corresponds to the x-value of 0 and the year 2010 corresponds to the x-value of 14 since 2010 - 1996 = 14. So, the two ordered pairs given in the problem are (0, 4.42) and (14, 7.89). i. To write the equation, we first find the slope. m = y2 - y1 x2 - x1 m = 7.89 - 4.42 14 - 0 m = 3.47 14 m ≈ 0.25 Begin with the slope formula. Let (x1, y1) = (0, 4.42) and (x2, y2) = (14, 7.89). Simplify the numerator and denominator. Simplify the result. One of the given points is (0, 4.42). This is the y-intercept; therefore, b = 4.42. Knowing the slope m = 0.25 and b = 4.42, the equation that models the average price of a movie ticket is y = 0.25x + 4.42. ii. The average price in 2015 is found by setting x = 19. y = 0.25x + 4.42 y = 0.25(19) + 4.42 y = 4.75 + 4.42 y = 9.17 Begin with the model. Replace x with 19. Multiply. Add. The average price of a movie ticket in 2015 will be $9.17. iii. To find when the average price is $10.67, we set y = 10.67 and solve for x. y = 0.25x + 4.42 10.67 = 0.25x + 4.42 10.67 - 4.42 = 0.25x + 4.42 - 4.42 6.25 = 0.25x 6.25 0.25 = 0.25x 0.25 25 = x Begin with the model. Replace y with 10.67. Subtract 4.42 from each side. Simplify. Divide each side by 0.25. Simplify. The average price of a movie ticket will be $10.67 in 25 years or in 2021. Student Check 5 Find the equation that represents each situation. Then use the equation to answer the questions. a. Ryan bought an SUV for $30,000. The value of the SUV decreases by $3000 each year. i. Write a linear equation that represents the value of the SUV, where x is the age in years. ii. Use the equation to find the value of the SUV after 4 yr. iii. When will the value of the SUV be $9000? b. In Fall 2000, there were approximately 15.3 million students enrolled in post-secondary degree granting institutions. In Fall 2009, there were


hendricks_beginning_algebra_1e_ch1_3
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