SlopeIntercept Form for the Equation of a Line
We have found the equation of a line in pointslope form and in standard
form.
Another form for the equation of a line is the slopeintercept form. We
can derive this from the pointslope form.
We begin with the pointslope form for the
equation of a line. Use the yintercept, (0, b), for the point (x_{1}, y_{1}).That is, substitute 0 for
x_{1} and b for y_{1}. 
y  y_{1}
y  b 
= m(x  x_{1})
= m(x  0) 
Simplify the right side.
Add b to both sides. 
y  b
y 
= mx
= mx + b 
Definition â€”
SlopeIntercept Form for the Equation of a Line
The slopeintercept form for the equation of a line with slope m and
yintercept (0, b) is:
y = mx + b
Example 1
Find the equation of the line with yintercept (0, 6) and slope 2.
Write the equation in slopeintercept form.
Solution
Substitute the given values in the
slopeintercept form of the equation.
Both the slope, m, and the yintercept, (0, b),
are given: m is 2 and b is 6.
Simplify. 
y = mx + b
y = 2x + (6)
y = 2x  6 
The slopeintercept form of the equation of the line with yintercept (0, 6)
and slope 2 is y = 2x  6.
Note â€” To Write the Equation of a Line Given Two Points
Here are two ways to write the equation of a line when given two
points:
Use the PointSlope Form
Step 1 Find the slope.
Step 2 Substitute the slope,
m, and the coordinates of
one of the points, (x_{1}, y_{1}), in
y  y_{1} = m(x  x_{1})
Step 3 Simplify. 
Use the SlopeIntercept Form
Step 1 Find the slope.
Step 2 Substitute the slope,
m, and the coordinates of
one of the points, (x, y), in y = mx + b
Then, solve the equation for b.
Step 3 Substitute the value of m
and the value b in y = mx + b. 
