How Does the Constant Product Formula (X Y=k) Govern the Price within a Liquidity Pool?

The formula ensures that the product of the quantities of the two tokens in the pool (x and y) always equals a constant value (k). When a trader buys token 'y' by depositing token 'x', the supply of 'x' increases and 'y' decreases.

To keep 'k' constant, the AMM automatically increases the price of 'y' relative to 'x'. This mechanism is how the pool algorithmically determines the asset price based on supply and demand.