My daughter is only 3 and a half. But she is more than willing to clean her room if we do it together. While I cook dinner she is eager to set the table and she eats 10x better if we eat together at the table instead of in front of the tv.
OK......a teenager and pre-schooler.,,,,far apart. But my point is that maybe since you are a single mom, like me, it is much easier to fix easy dinners and eat on the run instead of coming home and cooking dinner and spending that time together. I now have a housekeeper who does fix the dinner two nights a week and then I am off 2 days a week......so there is 4 easy days. Every day, we wake up and make her bed together, just to get into the habit. Today, we spent at least two hours organizing her play room. We ended up dancing and using tamborines and moroccas for another hour. So..........clean up, hopefully, is fun for her. Her bedroom is always clean. I don't let it get out of hand so she sees cleanliness as comforting.
A teen probably needs more time than a 3 year old, though. Talking, dancing, listening to music together. Don't worry about being her 'slave' ....worry about losing her friendship.