Intermediate Algebra (11th edition)

(a)Write an equation that models the data.

Since the points in FIGURE 33lie approximately on a straight line, we can write a

linear equation that models the relationship between year xand cost y. We choose two

data points, and to find the slope of the line.

The slope 93 indicates that the cost of tuition and fees increased by about $93 per

year from 2004 to 2009. We use this slope and the y-intercept to write an

equation of the line in slope-intercept form.

(b)Use the equation from part (a) to approximate the cost of tuition and fees in 2010.

The value corresponds to the year 2010.

Equation from part (a)

Substitute 6 for x.

Multiply, and then add.

According to the model, average tuition and fees for in-state students at public two-

year colleges in 2010 were about $2637.

y= 2637

y= 93162 + 2079

y= 93 x+ 2079

x= 6

y= 93 x+ 2079

1 0, 20792

m=

2544 - 2079

5 - 0

=

465

5

= 93

1 0, 2079 2 1 5, 2544 2 ,

168 CHAPTER 3 Graphs, Linear Equations, and Functions

NOW TRY

Writing an Equation of a Line That Models Data

Retail spending (in billions of dollars) on prescription drugs in the United States is

shown in the graph in FIGURE 34.

EXAMPLE 9

Year

Retail Spending on Prescription Drugs

Source: National Association of Chain Drug Stores.

Spending (in billions

of dollars)

300

250

200

150

100

50

0

2002 2003 2004 2005 2006 2007

183

259

FIGURE 34

(a)Write an equation that models the data.

The data increase linearly—that is, a straight line through the tops of any two

bars in the graph would be close to the top of each bar. To model the relationship

between year xand spending on prescription drugs y, we let represent 2002,

represent 2003, and so on. The given data for 2002 and 2007 can be written as

the ordered pairs and

Find the slope of the line

through and

Thus, spending increased by about $15.2 billion per year. To write an equation, we

substitute this slope and one of the points, say, 1 2, 183 2 ,into the point-slope form.

1 2, 183 2 1 7, 259 2.

m=

259 - 183

7 - 2

=

76

5

=15.2

1 2, 183 2 1 7, 259 2.

x= 3

x= 2

NOW TRY
EXERCISE 8
Refer to Example 8.

(a)Using the data values for
the years 2004 and 2008,
write an equation that
models the data.

(b)Use the equation from
part (a) to approximate
the cost of tuition and
fees in 2009.

NOW TRY ANSWERS

8. (a)
   (b)about $2445

y=73.25x+ 2079