In this talk we will present some preliminaries about affine manifolds such as a developing pair, and address the non-existence of certain affine manifolds whose holonomy has an invariant line. Specifically, we will show that if a closed affine manifold has holonomy inside the subgroup of affine automorphisms that preserve an affine line, then this manifold cannot be complete. From there, we analyze the situation where the affine holonomy preserves a parallel vector field and construct certain `large' open subsets on which the developing map is a diffeomorphism onto its image. This construction will be used to show the non-existence of a larger class of closed affine manifolds whose holonomy preserves an affine line.