6.6 Graphing Linear Equations 351 b) Using the slope determined in part (a) and the y-intercept, (0, 53), determine the equation of the line. y x 10.75 53 = + c) Using the equation you determined in part (b), determine the approximate test grade for a student who studied for 3 hours. 85.25 d) Using the equation you determined in part (b), approximate the amount of time a student would need to study to receive a grade of 80 on the biology test. 2.5 hours 105. Telephone Landlines The following graph was created with StatCrunch using data from the Federal Communications Commission website (FCC.gov). The dots on the graph show the number of non-cellular telephone landlines, in millions, in the United States for the years 2015–2021. The red line can be used to approximate this same number of landlines. On the graph, y represents the number of landlines, x 0 = represents the year 2015, x 1 = represents the year 2016, x 2 = represents the year 2017 and so on. Number of Landlines (in millions) Number of Telephone Landlines in the United States Years After 2015 1 2 3 4 5 6 100 105 110 115 120 125 0 Source: FCC.gov a) Use the points (0, 124) and (6, 97) to determine the slope of the red line. 4.5 − b) Determine the equation of the red line. y x 4.5 124 = − + c) Use the equation you determined in part (b) to estimate the number of landlines in the U.S. in 2018. 110.5 million landlines d) Assuming this trend continues, in what year will the number of landlines be approximately 70 million? 2027 106. e-Commerce The following graph was created with StatCrunch using data from the U.S. Department of Commerce (Commerce.gov). The term e-commerce refers to the trading of goods and services on the Internet. The dots on the graph show the revenue from e-Commerce, in billions of dollars, in the United States for the years 2020–2025. The red line can be used to approximate this $ same revenue. On the graph, y represents the revenue from e-Commerce in the U.S., x 0 = represents the year 2020, x 1 = represents the year 2021, x 2 = represents the year 2022 and so on. Revenue (in billions of dollars) Revenue from e-Commerce in the U.S. Years After 2020 1 2 3 4 5 600 700 800 900 1000 1100 1200 1300 0 Source: Commerce.gov a) Use the points (0, 617) and (5, 1264) to determine the slope of the red line. 129.4 b) Determine the equation of the red line. y x 129.4 617 = + c) Use the equation you determined in part (b) to estimate the revenue from e-commerce in the U.S. in 2021. $746.4 billion d) Assuming this trend continues, in what year will the revenue from e-commerce in the U.S. be approximately $1522.8 billion. 2027 Challenge Problems/Group Activities 107. a) Two lines are parallel when they do not intersect no matter how far they are extended. Explain how you can determine, without graphing the equations, whether the graphs of two different equations will be parallel lines when graphed. * b) Determine whether the graphs of the equations x y 2 3 6 − = and x y 4 6 6 = + are parallel lines. The lines are parallel. 108. In which quadrants will the set of points that satisfy the equation x y 1 + = lie? Explain. Quadrants 1, 2, and 4. The graph of the line x y 1 + = is in quadrants 1, 2, and 4; therefore, the set of points that satisfy the equation is in these quadrants. Research Activity 109. René Descartes René Descartes is known for his contributions to algebra. Write a paper on his life and his contributions to algebra. *See Instructor Answer Appendix
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