Just one line of each, or lots? It could be the display card, but it could also be the internal controller hardware of the display, or even the video cable! I am assuming here that the monitor is not the display of a laptop? Here is the workflow to determine the root cause:
If it is a laptop, stop and take it in for repair.
If it is a stand-alone monitor, first make sure the cable is properly attached to both ends, and that it isn't damaged.
The next thing to do is attach the monitor to another computer (using a different cable) and see if the problem persists.
If it does, you know the problem is with the monitor - get it fixed.
If it doesn't, then it is either the cable or the display adapter.
Swap out the cable first, and if the problem persists, you have a bad adapter.
If it is a bad adapter, then are you using a built-in video controller, or a separate card?