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 ( 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=3x2 .

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: m= 94 20 = 5 2

Then, write the equation: y= 5 2 x+4

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 y1=3(x+2) 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.

y1=3x6

Add 1 to both side.

y=3x5

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.