Header Recommendations for Certain Look

I’m trying to create a header but having issues. I want the black line to extend across the header, whether on desktop, tablet or mobile. So I loaded a background line image to go behind the logo, which has a black line in it. It’s not lining up properly when the screen is resized. Please see examples here:

http://taylorfx.com/header-issue/

The website I’m working on isn’t live. I’m not sure of the best way to go about achieving this look… Any help would be greatly appreciated!