How many distanct equivalence classes are picked out by this relation?

Question

Let $x\text{R}y \iff x-y=2k \quad k \in \mathbb{Z}$

How many distinct equivalence classes are there for this relation?

I want to say thre are as many equivalence classes as there are integers, but can't reason my way to that conclusion.

Answer 1

If $x$ and $y$ are integers, there are two equivalence classes: even and odd integers.