Explanation:
there is no big "trick" involved.
you just need to do the multiplication and then move the terms into the right spot, so that the x-, y- and constant terms are in the same place as the generic Ax + By = C
y + 5 = 4(x + 1)
y + 5 = 4x + 4
-4x + y = -1
or (after multiplying both sides by -1)
4x - y = 1
yes, B = 1 (or -1), so you could write 1y (or -1y) instead of only y (or -y).
but nobody does that.