Suppose that $M$ is a finitely generated module over $A=k[X_1,\ldots,X_n]$ of Krull dimension $m$ with $k$ an infinite field. Then one version of Noether normalisation says there is an $m$-dimensional $k$-subspace $W$ of the $k$-vector space spanned by $X_1,\ldots,X_n$ such that $M$ is finitely generated over $\operatorname{Sym}(W)$ considered as a subring of $A$.

As is surely well-known, in fact one can show that the set of $m$-dimensional $k$-vector spaces $W$ that work is open in the appropriate Grassmannian. My question is where is there a reference for this fact in the literature?