How do I convince my boyfriend I'm not cheating?

So my boyfriend just assumes that I cheated on him because he heard something when in actuality I would never cheat on anyone because I saw what it did to my mom when my dad cheated on her. I've been with my boyfriend for over a year and I'm terrified of losing him because I'm so in love with him and he's all I ever want in life. I have changed basically everything in my life just to be with him and now he wants to break up because of something he heard. Is there something I can say or do to prevent that from happening? All I can do right now is lay here and cry.