Writing Linear Equations in Slope-Intercept Form
Converting from Standard and Point-Slope Forms to
Slope-Intercept Form
Conversion from standard and point-slope forms to
slope-intercept 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 slope-intercept 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 slope-intercept form, with a slope of - 2
and a y-intercept of 3.
Key Idea
To convert from standard form to slope-intercept form,
• move the x term to the right-hand side of the equation,
and
• divide each side by the coefficient of y.
These steps for converting from standard form to
slope-intercept 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 slope-intercept 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 slope-intercept form of the equation. The slope is
4 and the y-intercept is 11.
Key Idea
To convert from point-slope form to slope-intercept form,
• use the Distributive Property to multiply through all
expressions in parentheses,
• remove the constant from the left-hand side, and
• divide each side by the coefficient of y.
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