Let $M$ be a set of straight lines. Define an EFL coloring of $M$ with $k$ colors as a function $f : P(M) \rightarrow \{ 1,2,\dots,k \}$, such that if two intersection points $p_1, p_2$ belong to the same line, then $f(p_1) \neq f(p_2)$. ($P(M)$ is the set of all intersection points of lines from $M$.) Denote by $\chi_E(M)$ the minimum number of colors needed for an EFL coloring of $M$. \
Question: Prove that the problem of finding $\chi_E(M)$ is NP-hard.\
Any helpful suggestion/hint would be greatly appreciated.