I got this black greenish line on my tooth right below the gum line. (photo)

There appears to be some recession (gum loss) in the area with moderate plaque and tarter accumulation in the area.  Tarter picks up food debris and amasses dark pigmented bacteria deposits.  I advice you to visit your dentist for a thorough exam of your mouth and gums and have a proper cleaning.

Hi:From the photo it appears that black greenish line to be tartar build up.  I would suggest to get a consultation with a dentist right away and you might need a deep cleaning to remove the tartar build up.  Best,Dr. Maddahi

You should see your dentist right away.  The picture is not real close and clear of the area but it appears that you may have a serious periodontal condition of the area.  This is not treatable with home remedies, you need professional help with this condition. 

certain types of bacteria in the mouth will cause the tartar or calculus to turn greenish in colour. This usually happens when plaque accumulates around the gums. If left unbrushed it will harden and form this greenish tint. 

The good news is that a registered hygienist or a professional cleaning at your dental office will remove this tartar and improve the health of your teeth and gums!