How Does Transaction Slippage Relate to the Size of the Liquidity Pool and the K Constant?

Slippage is the difference between the expected price of a trade and the executed price. It is inversely proportional to the size of the liquidity pool, which is represented by the k constant.

A larger k means deeper liquidity, so a given trade size causes a smaller change in the reserve ratio, resulting in lower slippage. Conversely, in a pool with a small k, the same trade size causes a significant shift in the reserves, leading to high slippage and a poor execution price for the trader.