2010 MacBook Air Black Horizontal Line Across the Screen
It's most likely your LCD screen.   

Your MBA has a single integrated GPU that's used for both your internal screen and to drive an external monitor.  The fact that it's not showing up on the external monitor narrows it down to the LCD screen.

Additionally, if this is happening prior to boot up of macOS, it's happening outside of the operating system so it's definitely a hardware issue.

It's possible to DIY replace the screen (Apple PN# 661-5732), but be aware that iFixit.com rates it as "difficult"