I think there must be more to the question than this -- there are rather a lot of equations relating x and y that one might come up with. Here are a few. y as a function of x: y = mx+c (straight line); y = x^2 (parabola); y = exp(x) (exponential). Curves: (x-h)^2 + (y-k)^2 = r^2 (circle), x^2/a^2 + y^2/b^2 = 1 (ellipse), xy=1 (rectangular hypberola), y^2 = x^3 + Ax + B (elliptic curve, NB not an ellipse), ...

Go to http://mathworld.wolfram.com/topics/Curves.html for a lot more about curves and their equations.