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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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