Let L denote the set of straight lines through the origin in $\displaystyle \mathbb{R}^2$. Let M denote the set of straight lines through (1,1) in $\displaystyle \mathbb{R}^2$. How many elements does $\displaystyle L \cap M$ have?

Is this just how many times the lines intersect? If so is it not just LxM intersections including the origin and (1,1), or, (LxM)-2 not including the origin of (1,1)?