MacBook Air reduces free space from 7GB to 1GB in after a few houres
Several things can use that much memory - before you reboot get a picture of a few things in terminal by pasting these commands and saving the results.


du -m /var/vm/*
vm_stat


You could also look at activity monitor and see how much memory on the left and how much swap is being used:



Then, you can see how much RAM you have, how much space will be needed for the sleep image or if some other process is using space. Also, check in the System Information - About This Mac window (the tool lives in /Applications/Utilities - choose Command I and then storage) to be sure you don't also have backups being stored locally. 

If you don't need them, you can turn off Time Machine and then turn it back on or use sudo tmutil disablelocal if you like terminal commands and know the risks of sudo and trusting someone on the internet giving advice.