The bulk of the stock Slackware PATH assignments are located in /etc/profile.d scripts. Those scripts are executed from within the /etc/profile script.
If your path assignments are system-wide and not specific to your normal user account, then create a new script in /etc/profile.d:
chmod +x /etc/profile.d/local.sh
Then add your new PATH variable as you desire:
Save the document.
If the PATH asssignments are specific only to y our normal user account, then place the commands in $HOME/.bashrc.
If you want more information about bash startup scripts:
Harmonizing the Bash Startup Scripts