Prove equivalence relationship

Question

How would I go about doing this?
I assume proving it's reflexive, symmetrical and transitive
Show that the relation $R = \{(x, y):3x − 5y \text{ is even }\}$ is an equivalence relationship.

Answer 1

Assuming $R \subset {\mathbb Z}^2$.

$3x-5y$ is even iff $3x$ and $5y$ are both even or both odd.

Terms are even iff respective variables are even, so the given relation is equivalent to 'both variables are even or both are odd'.

The three basic properties are obvious now.