Question

does air pressure increase with temperature

Answer 1

In a confined space such as in a closed bottle, when temperature increases, pressure increases too. 

But not in the open environment of our atmosphere. 

When air gets warmer, as it does often near the ground when the sun heats it, it gets lighter because less dense and it rises. 

As it does that, it cools down by the so-called adiabatic effect of coming into a lesser pressure. It it the same thermodynamic principle that is used in your fridge when a compressed coolant is released through a nozzle. 

Colder air can't contain so much moisture as warm and and when the temperature sinks to what is called the dew point temperature, moisture condenses into clouds. If the air keeps rising then the condensation continues and the drops get bigger until it starts raining. 

The reason the correct answer is: decrease is because, as air rises, the pressure decreases since it moves away. This is how low pressures are created and why low pressures are associated with clouds, precipitations and wind, this is the atmosphere filling in the void of the rising air.