Let us understand it as in the following equations-

Stating ideal gas equation, PV = nRT

So, we can say that, P x V ¤ T (direct proportionality)

So, P ¤ T/V 

Thus, there is an inverse proportionality between P and V.

This can also be understood theoretically. Consider an open vessel filled with gas molecules. Now say you apply pressure from the open top end of the vessel using a piston. What you are expected to observe is that there will be a decrease in the volume that is occupied by the gases, which reduces more as you increase the pressure. Thus, pressure and volume are inversely proportional.