Putting it here as a reminder. Been having this problem (default installation) since 10.0. Mysql comes default with Slackware as far as I can remember, but somehow not configured by default. Try to run Mysql right after installing and major fail awaits you. So here’s a little short guide on what to do post installation of Slackware 13.1 with Mysql.
chmod 755 / etc / rc.d / rc.mysqld
chown -R mysql:mysql / var / lib / mysql
chmod 755 / etc / rc.d / rc.mysql
/ etc / rc.d / rc.mysqld start
/ usr / bin/mysqladmin -u root password yourpassword