Are you speaking about your local or public IP address?
For the local address, it's as parman said, and that does not depend in any way your internet connection.
But the public IP address is given to you by your ISP, without any chance of having any fixed one. It really depends on what plan you have, for most home connections, IPs are dynamic, and static IPs are often for companies or more expensive plans. Unless you specifically ask for fixed IP, you're going to get a dynamic one.