First, you want to get it looking like y = mx + b, the original formula.
In y = mx + b, m = slope and b = y-intercept.
-3y + 21x = 15
(isolate the y, move the x to the right)
-3y = -21x +15
(isolate the y, divide by -3)
y = 7x - 5
Therefore, the slope is 7 and the y-intercept is -5.