Question

How are the pressure and volume of a gas related?

Answer 1

If the gas can be considered an ideal gas (a reasonable assumption in most cases), then the ideal gas law applies\[PV=nRT\]If the temperature is constant, then the right hand side of this equation is a constant. That implies that the product of the pressure and volume is a constant.

Answer 2

Using the result above (for a certain amount of a some gas, at a certain temperature ), we might set the righthand side to equal a constant, say K
\[PV = nRT = K\]
Then \[P =K/V\] or equivalently \[V = K/P\]

In otherwords, the pressure and volume of the gas are inversely proportional.