  We examine the incidence geometry of lines in the tropical plane. We prove
tropical analogs of the Sylvester-Gallai and Motzkin-Rabin theorems in
classical incidence geometry. This study leads naturally to a discussion of the
realizability of incidence data of tropical lines. Drawing inspiration from the
von Staudt constructions and Mn\"ev's universality theorem, we prove that
determining whether a given tropical linear incidence datum is realizable by a
tropical line arrangement requires solving an arbitrary linear programming
problem over the integers.
