You'd need to enable IP Forwarding on your Slackware router box:
This can be done with the following command.
echo 1 > /proc/sys/net/ipv4/ip_forward
and similarly, disabled by the following command:
echo 0 > /proc/sys/net/ipv4/ip_forward
when the box is restarted the enable command would need to be re-executed, so it may be an idea to put it in a script which is executed when the machine starts. rc.local for example.
Hope this helps. Good luck