To create a slide library, you need to be part of the Owners group on the SharePoint site. The person who created the site, the site administrator, is the one who determines this. Ask this person to give you permissions for the Owners group, if you don't have them already.
As a member of the Owners group, you'll have access to the Site Actions menu on the site. This menu enables you to create lists and libraries on the SharePoint site (document, picture, and slide libraries, for example).