I was reading some notes on affine algebraic geometry and came across the following fact:
If $k$ is a field with $\mathrm{char}~k = 0$, then if $V(f)$ is an irreducible hypersurface in $\mathbf{A}^n_k$, then there is a surjective linear projection $\pi: \mathbf{A}^n_k \to \mathbf{A}^{n-1}_k$ such that the composition $V(f) \to \mathbf{A}^n_k \to \mathbf{A}^{n-1}_k$ is finite.
Can someone point me to resource (book/lecture notes) where I can find this statement proved?