Along a two-phase coexistence curve, pressure and temperature change together. The Clapeyron equation relates the slope of that curve to the entropy and volume changes of the phase transition:

$$\frac{dp_{sat}}{dT}=\frac{s_g-s_f}{v_g-v_f}.$$

Using $h_{fg}=T(s_g-s_f)$ for reversible phase equilibrium gives

$$\frac{dp_{sat}}{dT}=\frac{h_{fg}}{T(v_g-v_f)}.$$

For liquid-vapor equilibrium, $v_g\gg v_f$ and $h_{fg}>0$, so saturation pressure normally increases with temperature.

The equation explains why boiling temperature depends on pressure: changing pressure moves the equilibrium state along the coexistence curve rather than changing temperature independently.

The Clapeyron equation is an equilibrium property relation. It does not predict the rate of boiling, condensation or nucleation; those require transport and kinetic information.