  We show that the empirical linear relation between the magnitude of the EMC
effect in deep inelastic scattering on nuclei and the short range correlation
scaling factor $a_2$ extracted from high-energy quasi-elastic scattering at
$x\ge 1$ is a natural consequence of scale separation and derive the
relationship using effective field theory. While the scaling factor $a_2$ is a
ratio of nuclear matrix elements that individually depend on the calculational
scheme, we show that the ratio is independent of this choice. We perform
Green's function Monte Carlo calculations with both chiral and Argonne-Urbana
potentials to verify this and determine the scaling factors for light nuclei.
The resulting values for $^3$He and $^4$He are in good agreement with
experimental values. We also present results for $^9$Be and $^{12}$C extracted
from variational Monte Carlo calculations.
