In this paper we show that the virial expansion up to third order for the osmotic pressure of a dilute polymer solution, including first-order perturbative corrections to the virial coefficients, allows for a scaling description of phase-separation data for polymer solutions in reduced variables. This scaling description provides a method to estimate the Theta-temperature, where demixing occurs in the limit of vanishing polymer volume fraction phi and infinite chain length N, without explicit assumptions concerning the chain-length dependence of the critical parameters T-c and phi(c). The scaling incorporates three limiting regimes: The Ising limit asymptotically close to the critical point of phase separation, the pure-solvent limit, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We incorporate the effects of critical and tricritical fluctuations on the coexistence-curve scaling by using renormalization-group methods. We present a detailed comparison with experimental and simulation data for coexistence curves and compare our estimates for the Theta-temperatures of several systems with those obtained from different extrapolation schemes.