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 (*x*_{1}, *y*_{1}) 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 = *3*x* – 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

**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* = –2*x* + 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.