Does it appear THE MOMENT you turn the unit on?
If it does, then you will have to run the monitor's self-test function by turning it on with the data cable (the one that does NOT connect to the power outlet) DISCONNECTED from the computer.
If the line still appears, then the monitor is faulty & cannot be "repaired". Usually, the entire LCD module is replaced.
If the line does not appear in the self-test mode, then check if it's connected to an ON-BOARD display adapter (typically found in the back of the machine, towards the middle area, towards where the ethernet cable and USB devices plug in) or a EXPANSION CARD (normally located towards the BOTTOM part in the back of the machine).
If it plugs in to the on-board slot, then the motherboard may be faulty. If it plugs in to an expansion card, then it's the card that may need to be replaced.
Of course, these are merely possibilities, but the most likely failing component here is the monitor itself. Busted display adapters very rarely, if at all, manifest these horizontal or vertical lines and STILL boot up. Regardless if it's on-board or expansion card, a failing display adapter would normally have either no display at all, or it would just simply stop booting up (screen remains dark: no lines).