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.
8x + 4y = 16
8x + 4y = 16 first subtract 8x
4y = -8x + 16 then divide all by 4
y = -2x + 4 slope form
6x + 3y = 21
6x + 3y = 21 subtract 6x
3y = -6x + 21 then divide all by 3
y = -2x + 7 slope form