i just got confused by why the equation looked different from the regular plane equation. i see that it's the same thing now. the book does refer to f_{x} and f_{y} as slopes tho.
For tangent plane equation
z-z0 = f{x}(x0,y0)(x-x0) + f{y}(x0,y0)(y-y0)
how come there is no cross product of the partial derivatives f{x} X f{y} to give the normal vector for the plane?