The price tag is not a contract and until a contract is executed nothing legally exists.
It takes an offer and acceptance.
If the price tag says $15,000 for the car, and you enter into a contract which the dealer signs then the dealer has to sell you the car. The same as if you make a mistake in your calculations and sign to purchase the car.
Now in the case where perhaps a dealer employee had changed the price and it could be proven that you knew that there would be some legal concept that allows the dealership to get out of the contract.
It takes an offer and acceptance.
If the price tag says $15,000 for the car, and you enter into a contract which the dealer signs then the dealer has to sell you the car. The same as if you make a mistake in your calculations and sign to purchase the car.
Now in the case where perhaps a dealer employee had changed the price and it could be proven that you knew that there would be some legal concept that allows the dealership to get out of the contract.