Writing Linear Equations in SlopeIntercept Form
Converting from Standard and PointSlope Forms to
SlopeIntercept Form
Conversion from standard and pointslope forms to
slopeintercept form is achieved by adding and subtracting terms
from each side of the equations, and then multiplying or
dividing. This is best illustrated using examples.
Example 1
Write 6x + 3y = 9 in slopeintercept form.
Solution
This equation is in standard form. Perform the necessary steps
to solve the equation for y.
6x + 3y 
= 9 

6x + 3y  6x 
= 9  6x 
Subtract 6x from each side. 
3y 
= 6x + 9 

y 
= 2x + 3 
Divide each side by 3. 
This equation is in slopeintercept form, with a slope of  2
and a yintercept of 3.
Key Idea
To convert from standard form to slopeintercept form,
• move the x term to the righthand side of the equation,
and
• divide each side by the coefficient of y.
These steps for converting from standard form to
slopeintercept form work whenever the coefficient of y is not
zero. If it is zero, the line is vertical and the slope is
undefined.
Example 2
Write 7( y  3) = 28( x + 2) in slopeintercept form.
Solution
To do this, first multiply through all the terms within
parentheses using the Distributive Property.
7( y  3) 
= 28( x + 2) 

7y  21 
= 28x + 56 
Distributive Property 
7y  21 + 21 
= 28x + 56 + 21 
Add 21 to each side. 
7y 
= 28 x + 77 

y 
= 4x + 11 
Divide each side by 7. 
This is the slopeintercept form of the equation. The slope is
4 and the yintercept is 11.
Key Idea
To convert from pointslope form to slopeintercept form,
• use the Distributive Property to multiply through all
expressions in parentheses,
• remove the constant from the lefthand side, and
• divide each side by the coefficient of y.
