When the temperature of a conductor rises, its resistivity and...

The conductivity $\sigma$ of a material is the reciprocal of its resistivity $\rho$, so $\sigma = \dfrac{1}{\rho}$.

The ratio of resistivity to conductivity is given by $\dfrac{\rho}{\sigma} = \dfrac{\rho}{1/\rho} = \rho^2$.

For a conductor, the resistivity $\rho$ increases with an increase in temperature.

Since $\rho$ increases, the square of the resistivity $\rho^2$ also increases.

Therefore, the ratio of resistivity to conductivity increases as the temperature rises.