How are pressure, volume and temperature related to the behavior of gases?

Pressure and volume of a gas are inversely related.  As one goes up, the other goes down, and vice-versa.  Pressing down on a bicycle tire pump illustrates that by decreasing the volume, squeezing the air into a smaller space, the pressure increases, and forces it through the hose into the tire.  This inverse relationship is summarized by

Pressure = 1/Volume   and   Volume = 1/Pressure  or

P= 1/V  and V = 1/P

This relationship can be summarized as the pressure times volume of initial conditions is equal to the pressure times volume of the final conditions, or

(Pressure 1)(Volume 1) = (Pressure 2)(Volume 2)

Adding the variable of temperature causes the volume and pressure to increase or decrease as the temperature increases or decreases.  The formula to describe that is a bit more complex, including n as the number of moles of the gas and R which is the gas constant:

(Pressure)(Volume) = (number of moles)(gas constant)(temp)

PV= nRT