If a relation is defined on the Cartesian plane by for some , what would the equivalence classes be? This seems like it should be easy, but I'm drawing a blank on it for whatever reason so for any help I would be grateful.
the equivalence class of some element on a set, is the set of all other elements in the set that relate to the said element under an equivalence relation.
so given any random point, it will relate to all points on the line i mentioned. that is, they will be equivalent under the given relation.