You have not provided details to the actual hardware you have, so we can't say with any certainty whether the drivers you have are correct, but the big three graphics providers are NVIDIA, AMD, and Intel.
As for Windows 7 specific drivers, the biggest category you want to look for is Vista x64 compatible, if you're running 64-bit Windows, or Vista x86 compatible for the 32-bit edition of Windows. Vista drivers should work all the way through Windows 8, with perhaps a few caveats.
While I don't mind helping you out with a few things, I disagree with your decision to downgrade your laptop from 8 or 8.1 to 7. You'll probably lose about 10% battery run-time doing so, as 8.x is a far more efficient, if not noticeably faster version of Windows.
Did you try to sort out the problems you were having with Windows 8.1 before you made the decision to downgrade to Windows 7? There's a good chance somebody in the forum here can help you sort out what you were experiencing, rather than dive into territory you seem to be unsure about. Did you consider just rolling back to and running Windows 8 as the manufacturer intended? And did you realize that unless Asus included a downgrade ability with your laptop, you will need to purchase a license for Windows 7 to be able to use it legally on your laptop. Your Windows 8 license does not grant you a license to use Windows 7 instead.