Section 3.5 Writing Equations of Lines 263 97. Shanika registers for her first semester in college. Her tuition includes fees of $400 plus $150 per credit hour. a. Write a linear equation that represents Shanika’s total tuition, where x is the number of credit hours Shanika will take. b. What is Shanika’s tuition if she registers for 12 credit hours? c. How many hours does Shanika take if her tuition is $1300? 98. James joins a fitness club. There is a one-time membership fee of $300 plus a monthly charge of $35. a. Write a linear equation that represents the total cost of joining the fitness club, where x is the number of months James is a member. b. What is the total cost of joining the fitness club for 1 yr? c. How many months has James been a member if this total cost is $1560? 99. Abdul purchases a new car for $20,000. The car’s value decreases by $1500 each year. a. Write a linear equation that represents the value of the car, where x is the age of the car in years. b. What is the car’s value after 6 yr? c. What will be the age of the car when its value is $5000? 100. One of the fastest growing counties in the United States is Flagler County, Florida. In 2004, its population was approximately 69,000. In 2010, the population was approximately 96,000. (Source: U.S. Census Bureau) a. Assuming this growth is linear, write an equation that approximates the population of Flagler County where x is the number of years after 2004. b. What is the estimated population of Flagler County in 2015? c. When will the population reach 150,000? 101. The number of single-family, existing homes sold in Florida in January 2010 was approximately 10,700. In January 2011, the number of homes sold was approximately 12,200. (Source: http://media.living.net) a. Assuming linear growth, write an equation that approximates the number of homes sold in Florida where x is the number of years after 2010. b. If this trend continues, how many homes will be sold in January 2015? 102. There were approximately 40 million Social Security beneficiaries in 1990 and approximately 61.4 million beneficiaries in 2012. (Source: www.ssa.gov) a. Write a linear equation that approximates the number of Social Security beneficiaries (in millions), where x is the number of years after 1990. b. If this growth continues, how many beneficiaries will there be in 2015? 103. The following graph shows the billions of dollars spent on spectator sports in the United States for the years 1990–2003. (Source: www.infoplease.com) 16 14 12 10 6 4.8 4 2 Billions Spent on Spectator Sports 7.4 11.5 13.5 14.1 8 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Years after 1990 a. Use the points (0, 4.8) and (13, 14.1) to write a linear equation that models the money spent on spectator sports (in billions of dollars) x years after 1990. b. If this growth continues, how much will be spent on spectator sports in 2015? 104. The median age of women at their first wedding was 20.3 in 1950. In 2010, the median age of women at their first wedding was 26.1. (Source: www.infoplease.com) a. Assuming linear growth, write an equation that represents the median age of women at their first wedding, where x is the number of years after 1950. b. Use the equation to predict the median age of women on the date of their first wedding in 2015. You Be the Teacher! Correct each student’s errors, if any. 105. Find the equation of the line that is parallel to 4x - 3y = 6 and passes through the point (8, 3). Vivian’s work: 4x - 3y = 6 -4x -4x -3y -3 = -4x -3 + 6 -3 y=- 4 3 x - 2. So, the slope is y=- 4 3 . Since it passes through the point (8, 3), the equation of the line is y=- 4 3 x + 3. 106. Find the equation of the line that passes through the points (-3, 4) and a0, 1 2 b . William’s work: m=- 7 6 and the equation is y=- 7 6 x + 4 107. Find the equation of the line with slope -2 that passes through the point (5, -1). Desi’s work: y = -2x - 1
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