Slope-Intercept Form

If you know the slope m, and y-intercept (0, b) of a line (the point where the line crosses the y-axis), you can write the equation of the line in slope-intercept form.

                        y = mx + b

(You can think of this as a special case of the point-slope form of the equation where (x1, y1) is the point (0, b).)

Example 1 :

Find an equation of the line in slope-intercept form with slope 3 and y-intercept (0, –2).

y = 3x – 2.

Example 2 :

Find an equation of the line in slope-intercept form with y-intercept (0, 4) and passing through the point (2, 9).

First, find the slope of the line:

Then, write the equation:

Equations in this form are easy to graph, since the slope of the line is m and the y-intercept of the line is b.

Example 3 :

Rewrite the equation in slope-intercept form.

The equation is already in point-slope form; we know that -3 is the slope.

Expand the right side using the distributive property.

Add 1 to both side.

Now we have the equation in slope-intercept form.

Example 4 :

Graph y = –2x + 3.

Since the equation is given in slope-intercept form, we know immediately that the line crosses the y-axis at (0, 3) and has slope –2. We can quickly use the slope to find a second point (1, 1), and graph the line.