Beginning Algebra, 11th Edition

The points appear to lie approximately in a straight line. We choose the ordered pairs

and from the table and find the slope of the line through these

points.

The slope, 347, is positive, indicating that tuition and fees increased each year.

Now use this slope and the point in the slope-intercept form to find an

equation of the line.

Slope-intercept form

Substitute for x, y, and m.

Multiply.

Subtract 1735.

Thus, and , so we can write an equation of the line.

To see how well this equation approximates the ordered pairs in the data table, let

(for 2003) and find y.

Equation of the line

Substitute 3 for x.

Multiply and then add.

The corresponding value in the table for is 4645, so the equation approximates

the data reasonably well. With caution, the equation could be used to predict values

for years that are not included in the table. NOW TRY

x= 3

y= 4797

y= 347132 + 3756

y= 347 x+ 3756

x= 3

y= 347 x+ 3756

m= 347 b= 3756

3756 =b

5491 = 1735 + b

5491 = 347152 +b

y=mx+b

1 5, 5491 2

$347

m= = 347

y 2 - y 1

x 2 - x 1

=

6185 - 5491

7 - 5

1 5, 5491 2 1 7, 6185 2

SECTION 3.4 Writing and Graphing Equations of Lines 217

x

y

(^01357)
6500
6000
5500
5000
4500
4000
3500
Year
Cost (in dollars)
AVERAGE ANNUAL COSTS AT
PUBLIC 4-YEAR COLLEGES
FIGURE 34
Let
and 1 5, 5491 2 = 1 x 1 , y 12.
1 7, 6185 2 = 1 x 2 , y 22

NOTE In Example 8,if we had chosen two different data points, we would have

found a slightly different equation.

NOW TRY ANSWER

8. ;
   The equation gives
   when , which approximates
   the data reasonably well.

x= 7

y= 6337

y= 423 x+ 3376

NOW TRY

EXERCISE 8

Use the points and

to write an equation

in slope-intercept form that

approximates the data of

Example 8.How well does

this equation approximate the

cost in 2007?

1 5, 5491 2

1 3, 4645 2