Point point form for the line through (a,b) and (c,d) is
(c-a)(y-b) = (d-b)(x-a)
We don't care about the constant part, this is
(b-d)x + (c-a)y = some constant
(a,b)=(5,-1) and (c,d)=(2,-5)
(-1 - -5) x + (2 - 5)y = some constant
4x - 3y = some constant
We didn't bother to calculate to constant because the parallel through (-1,8) means we get a different constant, obviously
4x - 3y = 4(-1) - 3(8)
4x - 3y = -28