It might be an idea to use dot notation for this.
If P is a plane, P.Lb is its x - y plane intercept.
The x - y plane is a plane with the formula z = 0. The x and y axes are lines on that plane.
P.Lb.m is the slope of P.Lb, Delta Y / Delta X.
P.Lb.b is the y intercept of P.Lb.
P.mz is the slope of P, Delta Z / Delta Y.
Given values x and y, to find a value z where (x, y, z) is a point on P, first we calculate a value y[b]:
y[b] = (P.Lb.m)x + P.Lb.b
Now, as an hypothesis, z = (y - y[b])P.mz.
The other alternative is z = (y[b] - y)P.mz.
How do I determine which it is?!
