In the Affine space $A$, given $m-$plane $\alpha$ and a point $P\notin\alpha$. Prove that there is only one $(m+1)-$plane containing $\alpha$ and $P$.
I can prove through $m+1$ independent points, there exists only one $m-$plane ($m\geq 0$), but I don't know how it can help prove this problem. Can anyone have any hints for me? Thanks!