How get my mom to say yes to letting me fly alone?

Okay so my family is moving to texas from maine and I am in 11th grade. I want to stay in maine for an extra month and then fly down so I can spend time with my friends and my boyfriend. I would pay for my own ticket and possibly the minor person thing where the flight attendant watches you. I just want more time to be away from my drunk and pothead father. I would be abl ed to stay with my grandma and aunt for the month.