Finding a complementary linear subspace to a variety of correct dimension in $\mathbb{P}^n$

Question

Let $k$ be an algebraically closed field. Let $V\subseteq \mathbb{P}^n$ be a projective variety of dimension $d\geq 0$. I want to show that there exists a linear subspace $L\subseteq \mathbb{P}^n$ of codimension $d+1$ such that $L\cap V=\emptyset.$

Edit: I've figured it out, following Mohan's comment.