I own my house and rent out a room in it. My roommate has been rude, and late with rent and utilities, I want to evict her. I have given her 45 days notice and she may leave sooner. The agreement we signed when she moved in said "45 days notice of the last renting day will be given by either party to end lease." It's very infomal. My question is: if she leaves early does she pay the rent for 45 days or am I responsible? Thanks.

What does the agreement say? If it is silent, then you will have to rely upon state law for termination of tenancy by the tenant. You are entitled to notice, also.

She pays but if she doesn't you could possibly be held responsible depending on your very informal lease.

If you giver her the option of vacating sooner then she doesn't pay after she moves.