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.