Morphism from the projective plane contracting a line

Every morphism $f:{\mathbb{P}}^2\to {\mathbb{P}}^n$ satisfies $f^{\ast }\mathcal{O}(1)\cong \mathcal{O}(d)$ for some $d\ge 0$. If $f$ contracts a line, restriction to that line makes $\mathcal{O}(d)$ trivial, hence $d=0$ and all defining sections are constant. Thus the entire morphism is constant.