Equivalence Relation: Proving R and Finding Class

[Pingunoot]

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Let X = R × R. Define the relation R on X as follows:
(x1 , y1 )R(x2 , y2 ) iff y1 − y2 = 2(x1 − x2 ).

(a) Is it an equivalence relation?
(b) If it is, what is the equivalence class of the point (3, 1)?

I've proved this for reflexive, but I'm not sure how to go about doing it for symmetric and transitive and finding the equivalence class :S

Any guidance would be much appreciated :)

 

[Dick]

Well, symmetric says (x1,y1)R(x2,y2) is equivalent to (x2,y2)R(x1,y1). What do those two conditions translate to? BTW, how did you prove reflexive?