Slope intercept form is: y = mx + b
So we have to move the variables around to get the form
4x - 3y = 9
Move the 4x to the other side
4x - 3y = 9
-4x -4x
So we get:
-3y = -4x + 9
Now let's isolate the -3 from the y by dividing it on both sides
-3y/-3 = -4x/-3 + 9/-3
That leaves us with:
y = 4/3x - 3