libmysqlclient_r.so.15 is included in:
- the mysql-5.0.81 package in Slackware-current and Slackware64-current
- the mysql-5.0.67 package in Slackware-12.2
And it is installed in /usr/lib/mysql in all cases.
<edit> /usr/lib64/mysql for Slackware64 of course... </edit>
I do not have access to a 12.1 machine at this moment, but I guess it is included in the mysql package as well.
Check if the file is there in your installation.
Run the following command to check if it is included in your mysql package:
grep libmysqlclient /var/log/packages/mysql*