1. EXAMPLE 3
Approximate a best-fitting line
Alternative-fueled Vehicles
The table shows the number y
(in thousands) of alternative-fueled
vehicles in use in the United States x years
after Approximate the best-fitting
line for the data. x 1 2 3 4 5 6 7 y
280
295
322
395
425
471
511
548

2. EXAMPLE 3
Approximate a best-fitting line
SOLUTION
STEP 1
Draw a scatter plot of the data.
STEP 2
Sketch the line that appears to
best fit the data. One possibility
is shown.

3. EXAMPLE 3
Approximate a best-fitting line
STEP 3
Choose two points that appear to lie on the line. For the
line shown, you might choose (1, 300), which is not an
original data point, and (7, 548), which is an original data
point.
STEP 4
Write an equation of the line. First find the slope using
the points (1, 300) and (7, 548).
248 6
m = =
548 – 300
7 – 1

4. Approximate a best-fitting line
EXAMPLE 3
Approximate a best-fitting line
Use point-slope form to write the equation. Choose
(x1, y1) = (1, 300).
y – y1 = m(x – x1)
Point-slope form
y – 300 = 41.3(x – 1)
Substitute for m, x1, and y1.
y x + 259
Simplify.
ANSWER
An approximation of the best-fitting line is y = 41.3x

5. EXAMPLE 4
Use a line of fit to make a prediction
Use the equation of the line of fit from Example 3 to
predict the number of alternative-fueled vehicles in use
in the United States in 2010.
SOLUTION
Because 2010 is 13 years after 1997, substitute 13 for x
in the equation from Example 3.
y = 41.3x = 41.3(13)

6. EXAMPLE 4
Use a line of fit to make a prediction
ANSWER
You can predict that there will be about 796,000
alternative-fueled vehicles in use in the United States in
2010.

7. EXAMPLE 5
Use a graphing calculator to find a best-fitting line
Use the linear regression feature on a graphing calculator
to find an equation of the best-fitting line for the data in
Example 3.
SOLUTION
STEP 1
Enter the data into two lists.
Press and then select Edit.
Enter years since 1997 in L1 and
number of alternative-fueled
vehicles in L2.

8. EXAMPLE 5
Use a graphing calculator to find a best-fitting line
STEP 2
Find an equation of the best-
fitting (linear regression) line. Press
choose the CALC menu, and
select LinReg(ax + b). The equation
can be rounded to y = 40.9x

9. EXAMPLE 5
Use a graphing calculator to find a best-fitting line
STEP 3
Make a scatter plot of the data pairs
to see how well the regression equation models the data.
Press [STAT PLOT]
to set up your plot. Then select
an appropriate window
for the graph.

10. EXAMPLE 5
Use a graphing calculator to find a best-fitting line
STEP 4
Graph the regression equation
with the scatter plot by entering the
equation y = 40.9x The graph
(displayed in the window 0 ≤ x ≤ 8 and
200 ≤ y ≤ 600) shows that the line fits
the data well.
An equation of the best-fitting line is y = 40.9x
ANSWER

11. GUIDED PRACTICE
for Examples 3, 4 and 5 4.
OIL PRODUCTION: The table shows the U.S. daily oil production y (in thousands of barrels) x years after 1994. a.
Approximate the best-fitting line for the data.
ANSWER
y = –130x

12. GUIDED PRACTICE
for Examples 3, 4 and 5 4.
OIL PRODUCTION: The table shows the U.S. daily oil production y (in thousands of barrels) x years after 1994. b.
Use your equation from part (a) to predict the daily oil production in 2009.
ANSWER
4760 gal

13. GUIDED PRACTICE
for Examples 3, 4 and 5 4.
OIL PRODUCTION: The table shows the U.S. daily oil production y (in thousands of barrels) x years after 1994. c.
Use a graphing calculator to find and graph an equation of the best-fitting line. Repeat the prediction from part (b) using this equation.

14. GUIDED PRACTICE
for Examples 3, 4 and 5
ANSWER