It doesn’t happen often, but whenever there’s a new kernel package for Slackware on my laptop I need to update the Broadcom driver. To do this:

1. Update your OS, as usual.
2. Reboot
3. Plug in the ethernet cable, if necessary
4. Login as root
5. Perform sbopkg -i broadcom-sta
6. Done

You can read more about it on the Slackware wiki here