Here's a conjecture I have. Can anyone prove or disprove it?
Given $n$ distinct straight lines in the plane, the total degree of any $n$ (or less) intersection points is O$(n)$ (where the degree of a point is the number of lines containing it).
Update: I meant the question as Justin Smith understood it. Pick any $n$ or less intersection points (actually they don't even have to be intersection points---just points in the plane). Then for each of these points, count how many lines contain it. Add up these numbers. The conjecture was that the sum will always be O$(n)$. Note that $n$ is both the number of lines and an upper bound on the number of points you are allowed to select.