I would like to resize my /var partition, but when I log on as root and try to umount it to resize it (using diskdrake), it says the device is busy. I cannot figure out how to umount it...
I thought about mounting /var it to a different partition (/vartemp), resizing /var and remounting to /var, but I dont have any extra space or any extra partitions. I would like to use what I have right now. Any suggestions? Thanks.

One thing to try is to boot in to single user mode. For slackware, it's runlevel 1. You can edit /etc/inittab which is very well documented for most distributions, then reboot. Be sure to change it back to whichever runlevel it was set at before when you're done doing your thing.

Or, you can go there directly after you boot up with 'telinit'. You'd still need to look in inittab for the runlevel numbers, though.

If you use telinit ('telinit 1'), do all your business there, then telinit back in to the multiuser session. There are two in slackware, 3 and 4, 4 starts up the X(K,G)DM session manager. HTH