A page to show all posts

I have the front page of my blog set up now to show teasers of the first few blog posts, which the user can then click one to read the full entry.

That’s on the front page. I’d like to create a link called “blog” that will take the user to a page similar this except that the full posts are shown.

So right now the front page that loads is index.php in my theme’s directory. Could I make a blog/index.php that is the same as that original index but instead shows the full posts?