After default installation of Slackware, MySQL can't be started correctly. We should do some work for initialization. The following steps have been tested on Slackware64 13.1. Remember to replace MYSQL_PASSWORD with your own password for root user of MySQL.
sudo -u mysql /usr/bin/mysql_install_db /etc/rc.d/rc.mysqld start /usr/bin/mysqladmin -u root password 'MYSQL_PASSWORD' /usr/bin/mysql_secure_installation
According to information during initialization, "/usr/bin/mysql_secure_installation" step is recommended for production servers.