Why Is the Constant Sum Formula Considered a “Linear” Pricing Model?

The constant sum formula (x+y=k) is considered a linear pricing model because it creates a straight-line pricing curve. The price of one asset in terms of the other is constant, regardless of the trade size.

This is because the formula dictates that for every one unit of asset x that is added to the pool, one unit of asset y must be removed to maintain the constant sum. This results in a 1:1 trading ratio, which is ideal for assets that are expected to have a perfectly stable price relationship, such as two stablecoins pegged to the same currency.