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EXAMPLE 3. Write an equation to model data. BIRD POPULATIONS.

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Write an equation to model data

BIRD POPULATIONS

The table shows the number of active red-cockaded woodpecker clusters in a part of the De Soto National Forest in Mississippi. Write an equation that models the number of active clusters as a function of the number of years since 1990.

Make a scatter plot of the data. Let xrepresent the number of years since 1990. Let yrepresent the number of active clusters.

EXAMPLE 3

Write an equation to model data

SOLUTION

STEP 1

Write an equation to model data

STEP 2

Decide whether the data can be modeled by a line. Because the scatter plot shows a positive correlation, you can fit a line to the data.

STEP 3

Draw a line that appears to fit the points in the scatter

plot closely.

STEP 4

Write an equation using two points on the line. Use

(2, 20) and (8, 42).

y2 – y1

11

22

m =

=

=

8 – 2

=

3

x2 – x1

6

y =

mx + b

Substitute for m, 2 for x, and 20 for y.

11

20 =

(2) + b

3

11

3

EXAMPLE 3

Write an equation to model data

Find the slope of the line.

Find the y-intercept of the line. Use the point (2, 20).

Write slope-intercept form.

b

38

11

38

11

38

3

3

3

3

3

x +

x + .

An equation of the line of fit is y =

ANSWER

The number yof active woodpecker clusters can be

modeled by the function y = where xis the number of years since 1990.

EXAMPLE 3

Write an equation to model data

Solve for b.

3. Use the data in the table to write an equation that models yas a function of x.

Sample answer: y = 1.6x + 2.3

ANSWER

for Example 3

GUIDED PRACTICE

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