normally, on a page where you insert a new blog article, you should build a select list for the category , populated from the categories table. You should have a primary key added in your categories table, this integer value will saved into your blog_articles table (called as an foreign key).
With a category list, you can pass this category ID , like: listarticles.php?catid=X
in listarticles.php you retrieve the passed ID in $_GET["catid"], you can list the articles table by this catid.