First* flight was a short hop PHX-LAX on HP, one of their $19 each way fares.
If your parents don't like you flying alone, have them consider the alternate. Me and my two brothers and sister took a flight to LAX together. My mom was nervous enough about having all her kids on one plane, then the night before there was the
USAir/Skywest crash at LAX. My mom about had a fit, but we went anyway.
*Actually I was on a flight as an infant, but don't remember it.