If you have the an equation of a line in point-slope form, say $f(x) = y = 3x + 1$ under what theory can you convert the f(x) to f(x,y) like
$f(x) = y = 3x + 1<br /> f(x, y) = 3x + 1 - y$

I understand it intuitively, I just don't understand the rules for when you can change the function arguments.