  The tight correlations between the masses of supermassive black holes (BHs)
and the properties of their host galaxies suggest that BHs coevolve with
galaxies. However, what is the link between BH mass ($M_{\rm BH}$) and the
properties of the host galaxies of active galactic nuclei (AGNs) in the nearby
Universe? We measure stellar masses ($M_*$), colors, and structural properties
for $\sim11,500$ $z\leq0.35$ broad-line AGNs, nearly 40 times larger than that
in any previous work. We find that early-type and late-type AGNs follow a
similar $M_{\rm BH}-M_*$ relation. The position of AGNs on the $M_{\rm BH}-M_*$
plane is connected with the properties of star formation and BH accretion. Our
results unveil the evolutionary paths of galaxies on the $M_{\rm BH}-M_*$
plane: objects above the relation tend to evolve more horizontally with
substantial $M_*$ growth; objects on the relation move along the local
relation; and objects below the relation migrate more vertically with
substantial $M_{\rm BH}$ growth. These trajectories suggest that radiative-mode
feedback cannot quench the growth of BHs and their host galaxies for AGNs that
lie below the relation, while kinetic-mode feedback hardly suppress long-term
star formation for AGNs situated above the relation. This work provides
important constraints for numerical simulations and offers a framework for
studying the cosmic coevolution of supermassive BHs and their host galaxies.
