Using a sample of nearby supernovae discovered in the Lick Observatory Supernova Search, Li et al. (2011) found that galaxies with higher stellar masses had lower supernova rates per unit mass for all types of supernovae. Using a code that detects and classifies supernovae in galaxy spectra, I have discovered a sample of ~135 Type Ia and II supernovae, which I use to measure supernova rates per unit mass as a function of galaxy stellar mass (as in Li et al. 2011), as well as star-formation rate (SFR) and specific SFR. I will show that the so-called "rate-mass relation" for Type Ia and Type II supernovae can be explained as a combination of the delay-time distribution (DTD) for each type of supernova and galaxy downsizing (i.e., massive galaxies tend to be older than less massive ones). For Type Ia supernovae, the observed rates are consistent with a power-law DTD with an index of -1, as observed in other types of surveys. For Type II supernovae, the DTD is limited to very short delay times so that the Type II supernova rates basically follow the star-formation rate.