Question

For an ideal gas, classify the following pairs of properties as directly or inversely proportional.

Answer 1

PT directly proportional 
PV inversely proportional 
TV directly proportional 
Pn direction proportional 
Vn directly proportional 

There are two easy ways to do this. The first is that, if two things are on the same side of the equation, they are inversely proportional (if one goes up, the other has to go down to keep the equation balanced), while if they are on opposite sides, they are directly proportional (if ones goes up, the other also has to go up, to keep it balanced). 

The other way is to imagine a scuba tank, and imagine you are doing everything to that tank. It becomes somewhat intuitive. 

What happens if the pressure in the scuba tank goes up? It is going to heat up. 

What if the pressure goes up and you can change the volume? The gas will expand and increase in volume. 

What if you increase the temperature? Again, gas expands, volume increases. 

What happens if you add more air to the tank? The pressure goes up.