  A galaxy's stellar mass-to-light ratio ($M_\star/L$) is a useful tool for
converting luminosity to stellar mass ($M_\star$). However, the practical
utility of $M_\star/L$ inferred from stellar population synthesis (SPS) models
is limited by mismatches between the real and assumed models for star formation
history (SFH) and dust geometry, both of which vary within galaxies. Here, we
measure spatial variations in $M_\star/L$ and their dependence on color, star
formation history, and dust across the disk of M31, using a map of
$M^\mathrm{CMD}_\star$ derived from color-magnitude diagrams of resolved stars
in the Panchromatic Hubble Andromeda Treasury (PHAT) survey. First, we find
comparable scatter in $M_\star/L$ for the optical and mid-IR, contrary to the
common idea that $M_\star/L$ is less variable in the IR. Second, we confirm
that $M_\star/L$ is correlated with color for both the optical and mid-IR and
report color vs. $M_\star/L$ relations (CMLRs) in M31 for filters used in the
Sloan Digital Sky Survey (SDSS) and Widefield Infrared Survey Explorer (WISE).
Third, we show that the CMLR residuals correlate with recent SFH, such that
quiescent regions are offset to higher $M_\star/L$ than star-forming regions at
a fixed color. The mid-IR CMLR, however, is not linear due to the high scatter
of $M_\star/L$ in star-forming regions. Finally, we find a flatter optical CMLR
than any SPS-based CMLRs in the literature. We show this is an effect of dust
geometry, which is typically neglected but should be accounted for when using
optical data to map $M_\star/L$.
