Let $X$ be a real vector space, $V\subseteq X$ a subspace, $p: X\to\mathbb{R}$ sublinear (\ref{def:sublinear_2025_08_19}), and $f: V\to\mathbb{R}$ linear with $f\le p$ on $V$. For any $x_0\in X\setminus V$ there exists $a\in\mathbb{R}$ and a linear map $F: V+\mathbb{R}x_0\to\mathbb{R}$ given by $F(v+tx_0)=f(v)+ta$ such that $F\le p$ on $V+\mathbb{R}x_0$ and $F\vert_V=f$.