Why Is the Price in an X Y=k Pool Always Quoted as the Ratio of the Reserves, Y/x?

The price of token X in terms of token Y is the marginal rate of substitution, which is approximated by the ratio of the reserves. To buy a small amount of token X, a trader must deposit an amount of token Y such that the product of the new reserves remains equal to k.

The required amount of Y is calculated based on the current reserve ratio, y/x. This ratio represents the effective price at that exact point on the curve, reflecting how many Y tokens are needed for one X token.