The equation xy=k represents a relationship where x and y are variables, and k is a constant. This can be interpreted as a function f(x, y) = k, where the output is the product of the inputs x and y. When solved for y, it reveals an inverse variation, expressed as y = k/x. The graphical representation of this equation is a hyperbola, indicating that as one variable increases, the other decreases. Overall, the interpretation of the equation can vary based on the context of the variables involved.