Q: My Apple TV (3rd) works fine with my new Macbook Air but doesn't show VIDEO with my 2009 MacBook Pro. Audio works with both. Can anyone help?

to do airplay mirror the video card needs to support realtime H.264 encoding older macs video card does not

you can read more here

Use AirPlay to see your Mac screen on an HDTV - Apple Support

for older macs and windows computers there are other programs which is suppose to make it happen such as airparrot

but the fact that they can't depend on the video card doing the encoding it will make performance worse as the main cpu will have to do all the work