Chap3 Section5

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 3.5 The Line of Best Fit 321 Version: Fall 2007 3.5 Exercises 1. The following set of data about re- volving consumer credit (debt) in the United States is from Google.com. This is pri- marily made up of credit card debt, but also includes other consumer non-mortgage credit, like those offered by commercial banks, credit unions, Sallie Mae, and the federal government. Year yrs x after 2001 all revolving credit C in billions of $ 2001 0 721 . 0 2002 1 741 . 2 2003 2 759 . 3 2004 3 786 . 1 2005 4 805 . 4 a) Set up a coordinate system on graph paper, placing the credit C on the vertical axis, and the years x after 2001 on the horizontal axis. Label and scale each axis appropriately. Draw what you feel is the line of best fit. Remember to draw all lines with a ruler. b) Select two points on your line of best fit that are not from the data table above. Use these two points to de- termine the slope of the line. Include units with your answer. Write a sen- tence or two explaining the real world significance of the slope of the line of best fit. c) Use one of the two points on the line and the slope to determine the equa- tion of the line of best fit in point- slope form. Use C and x for the de- pendent and independent variables, Copyrighted material. See: 1 respectively. Solve the resulting equa- tion for C and write your result using function notation. d) Use the equation developed in part (c) to predict the revolving credit debt in the year 2008. e) If the linear trend predicted by the line of best fit continues, in what year will the revolving credit debt reach 1.0 trillion dollars? 2. The following set of data about non- revolving credit (debt) in the United States is from Google.com. The largest compo- nent of non-revolving credit is automo- bile loans, but it is also includes student loans and other defined-term consumer loans. Year yrs x after 2001 Non- revolving debt D in billions of $ 2001 0 1121 . 3 2002 1 1184 . 1 2003 2 1247 . 3 2004 3 1305 . 0 2005 4 1342 . 3 a) Set up a coordinate system on graph paper, placing the non-revolving credit debt D on the vertical axis, and the years x after 2001 on the horizontal axis. Label and scale each axis appro- priately. Draw what you feel is the line of best fit. Remember to draw all lines with a ruler. b) Select two points on your line of best
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322 Chapter 3 Linear Functions Version: Fall 2007 fit that are not from the data table above. Use these two points to de- termine the slope of the line. Include units with your answer. Write a sen- tence or two explaining the real world significance of the slope of the line of best fit. c) Use one of the two points on the line and the slope to determine the equa- tion of the line of best fit in point- slope form. Use D and x for the de- pendent and independent variables, respectively. Solve the resulting equa- tion for D and write your result using function notation.
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