Generally, when I draw something to the screen, how do I get it off the screen again?

For example, I want to draw a line onto the screen, appearing at a source, which then moves to a target, then disappears (this is to simulate a "bullet-streak" fired from a source) I know how to do all the calculations i.e vectors and radians etc. But I don't know how to get the thing off the screen >.<

I'm using Python/Pygame. I really dont like Pygame but it's for Uni. I know not many people use Pygame, so if you give me an example in C++ that's fine.
Thanks !

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