There is no order book and nobody quoting a price. A pool holds two piles of tokens, multiplies them together, and refuses to let that product shrink. Everything else is arithmetic.
A pool holds 10 ETH and 30,000 USDC. Multiply them and you get k = 300,000, the number the contract will not let fall. The implied price is just the ratio of the reserves: 30,000 divided by 10, or $3,000 per ETH. No market maker set that. It's simply what's in the box.
— Educational, not financial advice.