For a first-order phase transition such as water to steam , we write Clausius-Clapeyron equation as:
$\frac{dP}{dT}= \frac{L}{T \Delta V}$
Now what I infer from this equation is that if the phase-transition takes place at a lower T (that is boiling point is lower) then the rate on the Left Hand Side increases which basically means that at that temperature any small change in T will cause high change in P. This inference is unsatisfactory to me and as such I want to understand what information this equation essentially gives.
More specifically, I wanted to understand a statement I had come across which said that this equation explains why boiling point of a liquid increases with increases in pressure. Although, physically I understand why this is true but how is this fact deduced from looking at the Clausius-Clapeyron equation?
I tried varying "stuff" in this equation to check whether I could get some sort of understanding but I just couldn't deduce that from this equation.