Hi, audkyrrie, you'd need a Thunderbolt 2 to HDMI 2.0 adapter plus an HDMI 2.0 cable long enough to reach your TV.....
I've enclosed an amazon Canada link for the adapter....depending on where you live, you may be able to get the same thing on Amazon USA......https://www.amazon.ca/Plugable-DisplayPort-Supports-displays-3840x2160/dp/B00S0BWR2K... you'd need to plug in the adapter and cable to both your MacBook AIr (2015) and your TV when both devices are turned off..... you'd be using the Thunderbolt 2 port/socket on your MacBook Air...after you've made the connection between the two, turn on your MacBook Air First, then turn on your TV set, then change the video input on the TV set to whichever one you plugged the HDMI cable into *the one that goes to the adapter which is plugged into your MacBook Air.... hopefully you should now see a picture.....
well, that's my best guess for today, anyways
John B