We show that a finite linear space with \(b = n^2 + n + 1\) lines, \(n \geq 2\), constant point-degree \(n+1\) and containing a sufficient number of lines of size \(n\) can be embedded in a projective plane of order \(n\). Using this fact, we also give characterizations of some pseudo-complements, which are the complements of certain subsets of finite projective planes.