Prove that if $\displaystyle a, b, c$ are not all zero, then the equation: $\displaystyle ax+by+cz+d=0$ represents a plane and $\displaystyle \langle a,b,c\rangle$ is a normal vector to the plane.

Hint if a $\displaystyle \neq$0, then $\displaystyle ax+by+cz+d=0$ is equivalent to $\displaystyle a(x+\frac{d}{d})+b(y-0)+c(z-0)=0$

My Calc III teacher loves proofs, but I'm not real good with them. How can I prove this? I'm not even sure how to approach it. Can anyone help? Thanks!