Comment by andrewflnr

The "graph" of a function is formally defined as exactly those points that make the equation true. https://en.wikipedia.org/wiki/Graph_of_a_function Granted, the graph is only one visualization of a function, and not the only valuable one.

Of course we also have to remember that functions are not the same as equations, and a given function, or more generally relation, can be represented by multiple different equations. For a trivial example, multiply both sides of your slashdot equation by a constant, or add x*y.