How do I point front page at index.php in theme directory

Hi I am stuck, I am trying to set static content as well as a slider on my homepage, when I go to settings and set a static homepage I use my slider so I edited index.php in the theme directory, but now WordPress refers to page.php instead and cannot get it to front page > index.php and other posts/pages > page.php even if I need a new php file, whatever it takes to get the homepage to look at a different template, could this be something to set from the database or another php file, if so, what am I looking out for?