Describing the equivalence classes (x, y)R geometrically.

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Let say (x, y) R (s, t) if x + t = y + s and I have already proven that R is an equivalence relation, however, I need to show the equivalence classes (x, y)R geometrically. How would I go about doing so?

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HINT: Let $a$ be any real number. What does the set $\{\langle x,y\rangle:y-x=a\}$ look like when you graph it in the plane?