Congruence modulo and equivalence classes

Hi,

**problem: **Suppose that $\displaystyle M$ is a subspace of a vector space $\displaystyle V$. Prove that a subset of $\displaystyle V$ is an equivalence class modulo $\displaystyle M$ if and only if it is a coset of $\displaystyle M$

**attempt: **

Let $\displaystyle N$ be a subset of $\displaystyle V$.

1st direction: If $\displaystyle N$ is a coset of $\displaystyle M$, then it is an equivalence class modulo $\displaystyle M$.

$\displaystyle N=x+M$.

Now, I don't really know how to go from N beeing a coset of M to it beeing an equivalence class modulo M. Any help is greatly appreciated!

Thanks.