How Does the Concept of “Slippage” Mathematically Relate to the Reserve Ratio Change?

Slippage is mathematically derived from the change in the reserve ratio caused by the trade. The initial price is the ratio of the reserves before the trade.

The final price is the ratio after the trade. Slippage is the difference between the initial price and the average execution price, which is a function of the path taken along the x y=k curve.

Larger reserve ratio changes, resulting from larger trades relative to the pool size, lead to higher slippage.