How do you write a standard form equation into slope intercept form?

Question

I know that slope intercept form is y=mx + b and standard form is Ax + By = C but I am having trouble rewriting from standard to slope intercept form. Any help would be very much appreciated!

Answer 1

A standard form equation is when it is set up

Ax + By = C.

6x + 2y = 4

A slope-intercept form equation is when it is set up y=mx+b.

Y = - 3x + 2

In order to go from one form to another, all you have to do is change the order of the given numbers.  First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it.  At this point your equation will be set up By = -Ax + C.  Then you want to divide the B from the By and the rest of the equation.  Therefore you will have y = - Ax/B + C/B.  This is the same thing as the slope-intercept form, just a few of the letters are different.

Example 1:         

Change from standard to slope form

         

8x + 4y = 16

8x + 4y = 16  first subtract  8x

4y = -8x + 16   then divide all by 4

y = -2x + 4   slope form

Example 2:

  6x + 3y = 21

6x + 3y = 21  subtract  6x

3y = -6x + 21  then divide all by 3

y = -2x + 7   slope form

Answer 2

 

Standard form line equation is Ax + By = C
To write the equation in slope-intercept form y = mx + b,

Subtract Ax form each side
Ax + By -Ax = C-Ax
By = -Ax + C
Divide each side by B
y = (-A/B)x + (C/B)
The slope intercept form line equation is
y = (-A/B)x + (C/B)