just did some research on grub for you, and it doesn't look too different from LILO. you want to find the menu.conf file, probably in /boot/grub, and here are some example entries:
The menu.conf file: this is used for booting multiple operating systems and menu building. Building the menu.conf file is not difficult. It uses plain English, as you will see in this section.
All the menu entries start with "title TITLENAME" without commas. You can set your TITLENAME to whatever you want.
To make the menu for booting Linux:
1. Set the title.
2. Set the root partition .
3. Set the kernel with right kind of parameters.
To make a working menu:
title Debian GNU/Linux 2.2 kernel 2.4.1
(Hash (#) in front of a line is a comment.)
To make a menu for Windows or DOS:
the naming convention seems to be different, hda1 = hd0,0 hda2 = hd0,1 hdb3 = hd1,2 etc etc.
the main thing is still to make a new entry with root pointing at your slackware partition.
i got the info from http://www.linuxgazette.com/issue64/kohli.html
which you can check out if you want.