Question

what is the relationship between air temperature and air pressure​

Answer 1

Pressure and temperature are related to each other by Gay-Lussac's Law. This law says that P1T1=P2T2, or the initial pressure multiplied by the initial temperature is equal to the product of the final temperature and the final pressure. Pressure and temperature have an inverse relationship. In other words, increasing one, will cause the other to decrease.

So if you increase the air temperature, the pressure is going to decrease. If you decrease the air temperature the pressure is going to increase.