1. EXAMPLE 4
Write an equation given two points
Write an equation of the line that passes through (5, –2)
and (2, 10).
SOLUTION
The line passes through (x1, y1) = (5,– 2) and
(x2, y2) = (2, 10). Find its slope.
y2 – y1
m =
x2 –x1
10 – (– 2) =
2 – 5 12
– 3
= – 4

2. Write an equation given two points
EXAMPLE 4
Write an equation given two points
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7).
y2 – y1 = m(x – x1)
Use point-slope form.
y – 10 = – 4(x – 2)
Substitute for m, x1, and y1.
y – 10 = – 4x + 8
Distributive property
y = – 4x + 8
Write in slope-intercept form.

3. EXAMPLE 5
Write a model using slope-intercept form
Sports
In the school year ending in 1993, 2.00 million females participated in U.S. high school sports. By 2003,the number had increased to 2.86 million. Write a linear equation that models female sports participation.

4. EXAMPLE 5
Write a model using slope-intercept form
SOLUTION
STEP 1
Define the variables. Let x represent the time (in years) since 1993 and let y represent the number of participants (in millions).
STEP 2
Identify the initial value and rate of change. The initial value is The rate of change is the slope m.

5. Write a model using slope-intercept form
EXAMPLE 5
Write a model using slope-intercept form
y2 – y1
m =
x2 –x1
2.86 – 2.00 =
10 – 0
Use (x1, y1) = (0, 2.00)
and (x2, y2) = (10, 2.86).
0.86 = 10
= 0.086
STEP 3
Write a verbal model. Then write a linear equation.

6. EXAMPLE 5
Write a model using slope-intercept form
y = x
ANSWER
In slope-intercept form, a linear model is
y = 0.086x

7. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
Write an equation of the line that passes through the given points.
6. (– 2, 5), (4, – 7)
SOLUTION
The line passes through (x1, y1) = (– 2, 5) and (x2, y2) = (4, – 7). Find its slope.
y2 – y1
m =
x2 –x1
– 7 – 5 =
4 – (– 2)
= – 2

8. GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line. Choose (x1, y1) = (4, – 7).
y – y1 = m(x – x1)
Use point-slope form.
y – 7 = – 2(x – 4)
Substitute for m, x1, and y1.
Simplify
y – 7 = – 2 (x + 4)
y + 7 = – 2x + 8
Distributive property
y = – 2x + 1
Write in slope-intercept form.

9. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
7. (6, 1), (–3, –8)
SOLUTION
The line passes through (x1, y1) = (6, 1) and
(x2, y2) = (–3, –8). Find its slope.
y2 – y1
m =
x2 –x1
– 8 – 1 =
– 3 – 6
– 9
= 1

10. GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line.
Choose (x1, y1) = (– 3, – 8).
y – y1 = m(x – x1)
Use point-slope form.
y – (– 8)) = 1(x – (– 3))
Substitute for m, x, and y1.
y + 8 = 1 (x + 3)
Simplify
y + 8 = x + 3
Distributive property
y = x – 5
Write in slope-intercept form.

11. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
8. (–1, 2), (10, 0)
SOLUTION
The line passes through (x1, y1) = (– 1, 2) and
(x2, y2) = (10, 0). Find its slope.
y2 – y1
m =
x2 –x1
0 – 2 =
10– (– 1) 2 11 –

12. GUIDED PRACTICE GUIDED PRACTICE for Examples 4 and 5
You know the slope and a point on the line, so use point-slope form with either given point to write an equation of the line.
Choose (x1, y1) = (10, 0).
y – y1 = m(x – x1)
Use point-slope form.
y – 0 = (x – 10) 2 11 –
Substitute for m, x, and y1.
y = (x – 10) 2 11 –
Simplify
y = 2 11 –
x + 20
Distributive property 2 11 –
x + 20 =
Write in slope-intercept form.

13. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
9. Sports In Example 5, the corresponding data for males are 3.42 million participants in 1993 and million participants in Write a linear equation that models male participation in U.S. high school sports.

14. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
SOLUTION
STEP 1
Define the variables. Let x represent the time (in years) since 1993 and let y represent the number of participants (in millions).
STEP 2
Identify the initial value and rate of change. The initial value is The rate of change is the slope m.

15. Write a verbal model. Then write a linear equation.
GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
y2 – y1
m =
x2 –x1
3.99 – 3.42 =
10 – 0
Use (x1, y1) = 3.42
and (x2, y2) = 3.99 =
STEP 3
Write a verbal model. Then write a linear equation.

16. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 4 and 5
y = x
ANSWER
In slope-intercept form, a linear model is
y = 0.057x