Slope-Intercept Form
If you know theslope , and -intercept of a line (the point where the line crosses the-axis), you can write the equation of the line inslope-intercept form.
(You can think of this as a special case of the点斜式of the equation whereis the point.)
Example 1:
Find an equation of the line in slope-intercept form with slopeand-intercept.
.
Example 2:
Find an equation of the line in slope-intercept form with-interceptand passing through the point.
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 and the-intercept of the line is .
Example 3:
Rewrite the equationin slope-intercept form.
The equation is already in point-slope form; we know thatis the slope.
Expand the right side using the distributive property.
Addto both side.
Now we have the equation in slope-intercept form.
Example 4:
Graph.
Since the equation is given in slope-intercept form, we know immediately that the line crosses the-axis atand has slope. We can quickly use the slope to find a second point, and graph the line.