= Solution
Let $I$ denote a characteristic <surface brightness> and $\Upsilon=M/L$ the relevant dynamical <mass-to-light ratio>. With comparable profiles, $L\propto IR^2$ and $M\propto V^2R/G$. Eliminating $R$ gives
$$
\boxed{L\propto\frac{V^4}{G^2\Upsilon^2 I}.}
$$
If both $I$ and $\Upsilon$ are independent of <speed>, converting <luminosity> to magnitude gives $M_V=\text{constant}-10\log_{10}V$. The empirical coefficient $-8$ instead means $L\propto V^{3.2}$, and therefore
$$
\boxed{\Upsilon^2 I\propto V^{0.8}.}
$$
For constant <surface brightness> this requires $\Upsilon\propto V^{0.4}$; for constant <mass-to-light ratio> it requires $I\propto V^{0.8}$. A mixture of these changes, including varying stellar populations or dark-matter fractions, can give the same observed slope. The simple derivation assumes comparable characteristic <radii> and structural coefficients.
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