How to Derive the Mass-Luminosity Relation for Main Sequence Stars?

[Pandabasher]

Homework Statement

The main sequence lifetime of a star, T, is related to it's luminosity, L, in an equation of the form T$\propto$L^-0.7
Use this equation to derive the form of the mass-luminosity relation for main sequence stars.


I know that I'm aiming for around L$\propto$M^3.5

Don't have a clue where to start, I know it'll be simple but I'm stuck.
Any help is greatly appreciated. Thanks, Matt.

 

[phyzguy]

If a star has luminosity L, at what rate is it consuming energy? How much stored energy does it have? How is the lifetime related to these two quantities?