Cauchy problem of a density probability

I can't find the solution for this Cauchy problem:

$$\frac{\partial \rho(q,p,t)}{\partial t} = - \frac{p}{m} \frac{\partial \rho(q,p,t)}{\partial q}$$ $$\rho(q,p,0) = \delta(q)g(p)$$ Probably the solution is $$\rho(q,p,t) = \rho(q-\frac{p}{m}t,p,0)$$ but I can't proof it. Anybody can help me?