Hello Gary1177,
Thanks for asking the Apple Support Communities about connecting your Mac to your TV. We have a few articles that may help.
Please start with this help article: Use your TV as a display with Mac - Apple Support
Next, check the adaptors and troubleshooting here: Connect to HDMI from your Mac - Apple Support
This article has more info specific info related to your MacBook Air, and even suggests another possibility if you have an Apple TV: Use an external display with your MacBook Air - Apple Support
"Tip: If you have an HDTV connected to an Apple TV, you can use AirPlay to mirror your MacBook Air screen on your TV screen in up to 1080p HD. See Use AirPlay on your Mac for details."
If you still need help, please go through the troubleshooting here: Get help with video issues on external displays connected to your Mac - Apple Support
Cheers.