I have read that equivalence partitioning can be used typically for intervals or lists, e.g. I assume it can be used for every set of inputs. Anyway if the requirement says that allowed colors are (RED,BLUE,BLACK, GREEN), I cannot treat them like a list, right? I mean, testing one of them would not be enough because developers most likely used some switch-case and thus it is not real "set" where one could represent also the others. So how it is meant with lists?

Also what is not that clear to me, I do not think it is always possible to do the initial partioning and then design the test cases.
What about checking two lines intersection: Y=MX+C. (two inputs)

1) The lines are paraller. M1=M1 but C1 must be different from C2.
2) Lines are intersecting. M1 must be different from M2.
3) Coincident. The are the same.

How can I use partitioning here? THis is actually taken from a book and it says that these sets are eq.classes.