NOW TRY194 CHAPTER 3 Linear Equations and Inequalities in Two Variables; Functions
OBJECTIVE 5 Use a linear equation to model data.
NOW TRY
EXERCISE 7
Use (a)the graph and (b)the
equation in Example 7to
approximate credit card debt
in 2006.
Using a Linear Equation to Model Credit Card DebtCredit card debt in the United States increased steadily from 2000 through 2008. The
amount of debt yin billions of dollars can be modeled by the linear equation
where represents 2000, represents 2001, and so on. (Source: The Nilson
Report.)
(a)Use the equation to approximate credit card debt in the years 2000, 2004, and 2008.
For 2000: Replace xwith 0.
For 2004:
For 2008:
y=940 billion dollars
y=32.0 182 + 684
y=812 billion dollars
y=32.0 142 + 684
y=684 billion dollars
y=32.0 102 + 684
x= 0 x= 1
y= 32.0x+684,
EXAMPLE 7
Replace xwith 4.2004 - 2000 = 4Replace xwith 8.2008 - 2000 = 8(b)Write the information from part (a) as three ordered pairs, and use them to graph
the given linear equation.
Since xrepresents the year and yrepresents the debt, the ordered pairs are
and
See FIGURE 15. (Arrowheads are not included with the graphed line, since the data are
for the years 2000 to 2008 only—that is, from x= 0 to x= 8.)
1 0, 684 2 , 1 4, 812 2 , 1 8, 940 2.
yx8509501000800900750
700
650
600(^01283)
Year
4567
U.S. CREDIT CARD DEBT
Debt (in billions of dollars)
y = 32.0x + 684
FIGURE 15
(c) Use the graph and then the equation to approximate credit card debt in 2002.
For 2002, On the graph, find 2 on the horizontal axis, move up to the
graphed line and then across to the vertical axis. It appears that credit card debt in
2002 was about 750 billion dollars. To use the equation, substitute 2 for x.
Given linear equation
Let.
Multiply, and then add.This result for 2002 is close to our estimate of 750 billion dollars from the graph.
y= 748 billion dollars
y= 32.0 122 + 684 x= 2
y= 32.0x+ 684
x= 2.
NOW TRY ANSWERS
- (a)about 875 billion dollars
(b)876 billion dollars
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