Recall that the slope-intercept form of a linear equation of a non-vertical line is given by:

Finding Slope-Intercept Form

y mx b

is the slope of th e e linm

is the y-intercept of the e0, linb

Example 1: Write the slope-intercept equation of the3

4.mline that contains the point (0 -5) and has slope

35

4y x

Substitute values into the equation …

y mx b

Note that the point (0 -5) is the y-intercept, so b = - 5.

Example 2: Write the slope-intercept equation of the line that contains the points (- 3, 8) and (0, - 2).

Now, find the slope of the line using the given points.

m 2 1

2 1

y y

x x

2 8

0 3

10

3

10

3

Note that the point (0 -2) is the y-intercept, so b = - 2.

102

3y x

Substitute values into the equation …

y mx b

10

3m 2b

Example 3: Write the slope-intercept equation of the line that contains the point (- 2, 5) and has slope m = - 4

Write the equation using the value given for the slope.

Note that the point (-2,5) is not the y-intercept, so we will need a different approach this time.

4y x b

y mx b

Now use the point to substitute values in for x and y.

4y x b

( , ) 2,5x y

5 4 2 b

5 8 b

3 b

4 3y x

Substitute for b in the above equation to get …