This paper is a contribution to the ongoing classification of finite linear spaces with line-transitive automorphism group. Let \(G\) be a group which acts line-transitively on a linear space \(\mathcal L\) and so that \(G\) acts imprimitively on the points of \(\mathcal L\). There are very few known examples, the only infinite family is constructed by considering projective planes. In 1989 \textit{A. Delandtsheer} and \textit{J. Doyen} [Geom. Dedicata 29, 307-310 (1989; Zbl 0673.05010)] proved a simple but very powerful result. Assume \(G\) is imprimitive with \(d\) sets of imprimitivity of size \(c\). Then there exist two natural numbers \(x\) and \(y\) so that \[ c=\frac{\binom{k}{2}-x}{y},\quad d=\frac{\binom{k}{2}-y}{x}, \] where \(k\) is the size of a line. In this paper the authors consider a number of interesting parameters which can be found using these ideas, especially useful when the imprimitivity comes from the orbits of a normal subgroup. They give very specific information for small values of the parameters and leave the reader with a number of interesting questions.