A standard form equation:
Ax + By = C
6x + 2y=4
Slope intercept equation:
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 B from 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 differ.