Convert from standard form to slope intercept form

To convert from standard form to slope intercept form you just need to solve for y using the standard form of the equation.

Example #1:

Convert the equation 4x + 2y = 12 to slope-intercept form

4x + 2y = 12

Subtract 4x from each side of the equation.

4x - 4x + 2y = 12 - 4x

0 + 2y = 12 - 4x

2y = 12 - 4x

2y = 12 + -4x

2y = -4x + 12

Divide each side of the equation by 2 so the equation can be written in slope-intercept form.

2y / 2 = (-4x + 12) / 2

y = -4x / 2 + 12 / 2

y = -2x + 6

The slope-intercept form is y = mx + b and m is the slope.

Comparing y = mx + b with y = -2x + 6, we can see that the slope is m = -2

The slope of the line is -2.

Example #2:

Convert the equation of -5x + 3y = 8 to slope intercept form

-5x + 3y = 8

Add 5x to each side of the equation.

-5x + 5x + 3y = 8 + 5x

0 + 3y = 8 + 5x

3y = 5x + 8

Divide each side of the equation by 3 so the equation can be written in slope-intercept form.

3y / 3 = (5x + 8) / 3

y = 5x / 3 + 8 / 3

y = (5 / 3)x + 8/3

The slope of the line is 5 / 3.

Convert from standard form to the slope-intercept form: the general form

Example #3:

Find the slope of Ax + By = C

Ax + By = C

Subtract Ax from each side of the equation.

Ax - Ax + By = C - Ax

0 + By = C - Ax

By = C - Ax

By = C + -Ax

By = -Ax + C

Divide each side of the equation by B so the equation can be written in slope-intercept form.

By / B = (-Ax + C) / B

y = -Ax / B + C / B

y = (-A / B)x + C / B

The slope of the line is -A / B.