Hertzsprung-Russell slope of a stellar homology sequence ($d\log L/d\log T_{\mathrm{eff}}=4Y/(Y-2X)$)

For a stellar homology sequence with $R\propto M^X$ and $L\propto M^Y$, the Stefan–Boltzmann law gives $T_{\mathrm{eff}}\propto M^{(Y-2X)/4}$. Eliminating mass gives the displayed Hertzsprung-Russell diagram slope when $Y\ne 2X$. The usual horizontal axis decreases in temperature toward the right, reversing the visual left-to-right sign. The relation is between logarithmic variables and depends on the specified structural assumptions.