The Walecka model contains essentially two parameters that are associated with the Lorentz scalar (S) and vector (V) interactions. These parameters are related to a two-body interaction consisting of S and V, imposing the condition that the two-body binding energy is fixed. We have obtained a set of different values for the nuclear matter binding energies (B N) at equilibrium densities (rhoo). We investigated the existence of a linear correlation between B N and rhoo, claimed to be universal for nonrelativistic systems and usually known as the Coester line, and found an approximate linear correlation only if V - S remains constant. It is shown that the relativistic content of the model, which is related to the strength of V - S, is responsible for the shift of the Coester line to the empirical region of nuclear matter saturation.