Why Does the Price of a Large Trade Deviate More Significantly from the Spot Price Y/x?

The AMM's constant product formula, x y = k, is a curve. When a large trade is executed, the pool must move further along this curve to satisfy the trade, significantly altering the ratio of x and y reserves.

This large alteration in the reserve ratio means the effective average price of the trade is much higher (or lower) than the instantaneous spot price (y/x) at the start of the trade, leading to high slippage.