on your monitor make sure your display does not run off the sides of the screen. i have seen monitors "ghost" on the edges if that happens. if you find that may be the case you can adjust it using the on screen menu/dials on the monitor.
if that is not the case. try your monitor on another system if you can. if it is still there more than likely(but not definitely) you have a problem with the monitor.
if the line disappears when using on another system. this points to the vid card or settings on your system. check these things and maybe someone else can help you more.