Strong Seperation between hypreplane and an affine subspace

Question

Let $h \in \mathbb{R}^n\backslash \{0\}$ and $r \in \mathbb{R}$. A sure that $M$ is an affine subspace of $\mathbb{R}^n$ with $H(h, r) \cap M=\phi$. I tried to use Banach separation theorem to show that there is some hyperplane in $\mathbb{R}^n$, which strongly separates $H(h, r)$ and $M$, but it did not work. How can I prove this or maybe disprove it?