  We present a model for the origin of the extended law of star formation in
which the surface density of star formation ($\Sigma_{\rm SFR}$) depends not
only on the local surface density of the gas ($\Sigma_{g}$), but also on the
stellar surface density ($\Sigma_{*}$), the velocity dispersion of the stars,
and on the scaling laws of turbulence in the gas. We compare our model with the
spiral, face-on galaxy NGC 628 and show that the dependence of the star
formation rate on the entire set of physical quantities for both gas and stars
can help explain both the observed general trends in the
$\Sigma_{g}-\Sigma_{\rm SFR}$ and $\Sigma_{*}-\Sigma_{\rm SFR}$ relations, but
also, and equally important, the scatter in these relations at any value of
$\Sigma_{g}$ and $\Sigma_{*}$. Our results point out to the crucial role played
by existing stars along with the gaseous component in setting the conditions
for large scale gravitational instabilities and star formation in galactic
disks.
