ABSTRACT Over the past half century, gas outflows and winds have been observed as asymmetric emission lines in a wide range of astrophysical contexts, including galaxies and early-type stars. While P Cygni lines are modeled and understood with physically motivated profiles under the Sobolev approximation, asymmetric nebular lines are not. Previous studies of galactic outflows using nebular emission lines have made physically unjustified assumptions about the shape of the line profile. These approaches limit assessment of outflow properties and do not connect observations to the underlying physics. The physical complexity of galactic outflows requires a more robust approach. In response to this need, we present a novel profile for modeling nebular emission lines which is generalized yet physically motivated and provides insight into the underlying mechanisms of galactic outflows. To demonstrate the usefulness of this profile, we fit it to the asymmetric nebular lines observed in the nuclear region of Mrk 462, a starburst-active galactic nucleus composite galaxy. From analysis of the best-fitting profile, we conclude that the observed profile arises from a dusty radiation-pressure-driven outflow with a terminal velocity of $750\rm ~km \, s^{-1}$. This outflow, while weak by some standards, is still sufficiently strong to regulate star formation and black hole growth in the host galaxy by removing gas from the inner few kiloparsecs. Outflows like the one we observe and characterize in Mrk 462 are crucial to our understanding of episodic gas-fueled activity in galactic nuclei, which undoubtedly plays a pivotal role in galaxy evolution.