I know this is easy, but I can't find the way to prove this:

Let $\displaystyle lV,\Vert . \Vert _V) \longrightarrow (W,\Vert . \Vert _W)$ be a linear transformation. Show that if $\displaystyle l$ is continous at $\displaystyle 0$ then there exists $\displaystyle c>0$ such that $\displaystyle \Vert l(v) \Vert _W \leq c \Vert v \Vert _V \forall v \in V$