Is the morphism of affine varieties given by Noether Normalisation a closed map?

Question

Let $X\subseteq \mathbb A^n(k)$ be an affine variety over the algebraically closed field $k$. Then by the geometric interpretation of Noether Normalisation Lemma there is a finite and surjective morphism $\varphi:X\to \mathbb A^m(k)$, where $m$ is the dimension of $X$ (see here for the process noether normalization theorem geometric meaning).

Is it true that the morphism $\varphi:X\to \mathbb A^m(k)$ is a closed map?

Answer 1

Any finite morphism is proper (hence universally closed).