We show that the law of linearity for a unit Compressibility factor testifying a lot of experimental data for many substances can be provided by appropriate procedure following from the rigorous consequences of statistical mechanics, namely, the virial expansion. An equation of state that includes the terms up to the fourth power of density is obtained by using second and third virial coefficients. The critical point parameters, phase densities, and pressure along the liquid-gas coexistence curve for the Lennard-Jones (6-12) (LJ) and Buckingham (exp6) potentials are defined. The results corresponding to the LJ potentials are in good agreement with the solution of integral equations and simulation results. For the Buckingham potentials, our predictions agree well with the experimental data for the group of real substances, satisfying the law of corresponding states.