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```									Lesson 4-2

Example 1 Write an Equation Given the Slope and a Point
1
Write an equation of a line that passes through (–1, 2) with a slope of .
4
Step 1 Find the y-intercept.
y = mx + b          Slope-intercept form
1                               1
2 = (-1) + b        Replace m with 4, y with 2, and x with –1.
4
1
2 = -4 + b          Multiply.
1 1          1           1
2 + 4 = -4 + b + 4      Add 4 to each side.
9
4=b                 Simplify.

Step 2    Write the equation in slope-intercept form.
y = mx + b Slope-intercept form
1 9                        1            9
y = 4x + 4    Replace m with 4 and b with 4.
1   9
Therefore, the equation of the line is y = x + .
4   4

Example 2 Write an Equation Given Two Points
Write an equation of the line that passes through each pair of points.
a. (8, 6) and (0, 3)
Step 1    Find the slope of the line containing the given points.
y2 - y1
m= x -x            Slope Formula
2   1
3-6
=               (x1, y1) = (8, 6) and (x2, y2) = (0, 3)
0-8
-3 3
= -8 or 8       Simplify.

Step 2    Use the slope and either of the two points to find the y-intercept.
y = mx + b          Slope-intercept form
3=    8  (0) + b
3                            3
Replace m with 8, x with 0, and y with 3.
3=0+b                Simplify.
3=b                  Simplify.
Step 3    Write the equation in slope-intercept form.
y = mx + b        Slope-intercept form
3                              3
y = 8x + 3        Replace m with 8 and b with 3.

3
Therefore, the equation of the line is y = 8x + 3.
b. (-2, -7) and (1, 5)
Step 1    Find the slope of the line containing the given points.
y2 - y1
m=              Slope Formula
x2 - x1
5 - (-7)
= 1 - (-2)   (x1, y1) = (-2, -7) and (x2, y2) = (1, 5)
12
= 3 or 4     Simplify.

Step 2     Use the slope and either of the two points to find the y-intercept.
y = mx + b        Slope-intercept form
5 = (4)(1) + b    Replace m with 4, x with 1, and y with 5.
5=4+b             Simplify.
5–4=4+b–4             Subtract 4 from each side.
1=b               Simplify.
Step 3     Write the equation in slope-intercept form.
y = mx + b      Slope-intercept form
y = 4x + 1      Replace m with 4 and b with 1.

Therefore, the equation of the line is y = 4x + 1.
Real-World Example 3 Use Slope-Intercept Form
RUNNING In 1975, the World record for the one-mile run was 3 minutes 51 seconds. In
1999, the world record was approximately 3 minutes 43 seconds. Write a linear equation
that could be used to estimate the world record time, in seconds, for any year after 1975.
Understand        You know the time in 1975 is 3 minutes 51 seconds or 231 seconds. You know
the time in 1999 is 3 minutes 43 seconds or 223 seconds.
Plan              Let x represent the year after 1975. Let y represent the time in seconds. Write an
equation of the line that passes through the points (0, 231) and (24, 223).
Solve             Find the slope.
y -y
m = x2 - x1             Slope formula
2    1
223 – 231
= 24 – 0              Let (x 1 , y 1 ) = (0, 231) and (x 2 , y 2 ) = (24, 223).
–8       1
= 24 or –3            Simplify.

Choose (0, 231) and find the y-intercept of the line.
y = mx + b          Slope-intercept form
1                               1
231 = –3(0) + b         Replace m with -3, x with 0, and y with 231.
231 = b                 Simplify.
1
Write the equation using m = –3 and b = 231.
y = mx + b          Slope-intercept form
1                                  1
y = –3x + 231       Replace m with -3 and b with 231.
1
Therefore, the equation is y = –3x + 231.

Check       Check your result by using the coordinates of the other point.
1
y = –3x + 231           Original equation
1
223      –3(24) + 231       Replace y with 223 and x with 24.

223 –8 + 231                Multiply.
223 = 223                  Simplify.

Real-World Example 4 Predict from Slope-Intercept Form
RUNNING Use the equation in Example 3 to predict the world record time for the
one-mile run in 2008.
1
y = –3x + 231             Original equation
1
y = –3(33) + 231          Replace x with 2008 – 1975 or 33.
y = 220                   Simplify.

Using the equation, an estimate of the world record in 2008 is 220 seconds or 3 minutes
40 seconds.

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