Changing text and tag line on header

I’m using a basic twenty-ten word press theme. I’ve been using it only for a blog, and I’m changing it over to a web site that I’m using the one column, one sidear template to create the static pages for. I want to use the same header image througout the web, but I only want the current site title and the current tag line on the blog pages. I want to put some simple text on the current header image, and have that header image appear on all pages, both the static web pages and the blog pages. Don’t know a lot about working with the code, but willing to learn. Any help is appreciated.
Thanks.