Using a method to discover and classify supernovae (SNe) in galaxy spectra, we detect 91 Type Ia SNe (SNe Ia) and 16 Type II SNe (SNe II) among ∼ 740 000 galaxies of all types and ∼ 215 000 star-forming galaxies without active galactic nuclei, respectively, in Data Release 9 of the Sloan Digital Sky Survey. Of these SNe, 15 SNe Ia and 8 SNe II are new discoveries reported here for the first time. We use our SN samples to measure SN rates per unit mass as a function of galaxy stellar mass, star-formation rate (SFR), and specific SFR (sSFR), as derived by the MPA-JHU Galspec pipeline. We show that correlations between SN Ia and SN II rates per unit mass and galaxy stellar mass, SFR, and sSFR can be explained by a combination of the respective SN delay-time distributions (the distributions of times that elapse between the formation of a stellar population and all ensuing SNe), the ages of the surveyed galaxies, the redshifts at which they are observed, and their star-formation histories. This model was first suggested by Kistler et al. for the SN Ia rate-mass correlation, but is expanded here to SNe II and to correlations with galaxy SFR and sSFR. Finally, we measure a volumetric SN II rate at redshift 0.075 of R II,V = 0.621