Slopeintercept Form for the Equation of a Line
If we take the equation of a line and solve it for y we get the slopeintercept form for the equation of a line.
Definition
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 a line in slopeintercept form that has slope m = 2 and yintercept (0,
3).
Solution 
y = mx + b 
The point (0, 3) has the form (0, b). So, b is 3. 
Thus, replace m with 2 and b with 3. 
y = 2x  3 
The slopeintercept form for the equation of this line is
y = 2x  3 
Example 2
Write the equation 4x  3y = 12 in slopeintercept form.
Solution 
4x  3y 
= 12 
Solve the given equation for y.

Subtract 4x from both sides. 
3y 
= 4x + 12 
Divide both sides by 3. 


Simplify. 
y 

So, the equation in slopeintercept form is
.
The slope of this line is
and the yintercept is (0,
4).
Example 3
Find the slopeintercept form for the equation of the line that passes
through the points (6, 1) and (2, 5).Solution
First, we need to find the slope, m.
In the slope formula, let (x_{1}, y_{1}) = (6, 1) and (x_{2}, y_{2})
= (2, 5).
So, the slope is
.
Note:
You can use either point (x_{1}, y_{1}) and (x_{2}, y_{2}).
Next, use the pointslope formula.

y  y_{1} 
= m(x  x_{1}) 
Let (x_{1}, y_{1}) = (6, 1) and

y  1 

y  1 

Then, solve for y.

Distribute
on the right side.

y  1 

Add 1 to both sides. 
y 

So, the slopeintercept form for the equation
Note:
You can also write
in standard
form, Ax + By = C. To do this, subtract
from both sides to
get
Now, multiply both sides by 2 to get:
x + 2y = 8
