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 nonmortgage
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,
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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 nonrevolving credit is automo
bile loans, but it is also includes student
loans and other definedterm 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 nonrevolving 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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 Slope, Fahrenheit, best fit, Linear function

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