Before you run to the tool store to rent a snake, check with your city sewer department. Not sure if it's the norm, but here in Cincinnati, if you're having issues with your sewer you can call the sewer district and they'll come out and check it. Theoretically, they only check from the main to the right-of-way but in reality there's not real way of knowing when you get there so they end up checking up all the way to the house. It's also a one time thing.
How old is the house? If there were problems with back-ups in the past, the city could have put in a back flow preventer on the floor drain. That's a very popular band aid here where there are still a lot of combined sewers.