How Does a “Bonding Curve” Visually Represent the X Y = K Relationship?

A bonding curve is a graph where the x-axis represents the reserve of one token (x) and the y-axis represents the reserve of the other token (y). The $x times y = k$ formula produces a hyperbolic curve.

Any point on this curve represents a valid state of the pool, and the movement along the curve during a trade visually represents the price change and the resulting token ratio adjustment.