Implicit Planes — How It Works II

If   f(x,y,z) = ax + by + cz - d   then we can obtain the coefficients from:

a =f(1,0,0) - f(0,0,0)
b =f(0,1,0) - f(0,0,0)
c =f(0,0,1) - f(0,0,0)
d =-f(0,0,0)

Now check if  f(x,y,z)  actually does equal  ax + by + cz - d  for the determined coefficients, and if so, check that a, b, c and d are multiples of the professor's coefficients.