Q: macbook air wont work with data projector

If audio is needed, you'll need to more closely identify which MacBook Air you have:

About Mini DisplayPort to HDMI adapters

How to find your Mac's model and age?

If your MacBook Air is older than July 20, 2011, you'll need to identify whether or not it has a mini-Displayport, or a mini-DVI port:

mini-DVI

mini-Displayport

All technologies work well with the video of DVI or HDMI with the right adapter.  VGA and S-Video you need the proper adapter, and you won't necessarily have all available resolutions that are lower.