Does GeoGebra run on Linux?

The practical answer for a student on Linux is to use geogebra.org in a browser. The Calculator Suite, Classic, Graphing, Geometry and the rest all run there, and GeoGebra's download page offers a browser start as the first option on every platform. Your browser can pin it so it opens in its own window and appears in the applications menu like a normal app.

The installed version is the weak spot. GeoGebra's installation documentation lists Windows and Mac installers for the current apps, and for Linux only a portable bundle of the older Classic 5 release, marked unsupported. It is there if you need offline work on an old machine, but it is not the version anyone is maintaining.

In practice the browser version works offline once it has loaded, because it installs itself as a web app, so the usual reason for wanting a download mostly goes away.

Your .ggb files carry across. They open in the browser version the same way they opened on Windows, and files saved to a GeoGebra account are already waiting when you sign in on the new machine.