The time resolved inhomogeneous broadened line shape is derived from analytical theory for a liquid which exhibits spatial heterogeneity regarding the solvent response times. The results demonstrate that it is the heterogeneous nature of supercooled liquids which gives rise to asymmetric lines and to a maximum in the linewidth as a function of time while the average emission energy experiences a redshift. The time dependence of the calculated and of the observed linewidths agree quantitatively, but differ significantly from the behavior expected for systems with homogeneous dynamics.