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.