Even though your ticket says three points, if you are like it is here, because you are a minor, it is actually double the points on your license. I am not sure if this is the case for you or not. Contact the courthouse office and ask to speak to whoever would be handling your case ASAP. Things are handled differently in different states, but you should talk with the DA or assistant DA to find out what you can plea it down to. They only know about what the ticket is written up as at this point and have not talked to the cop about your ticket and usually they do not until you get to court. Just explain to them that you would pay a fine if necessary, but dont want the points on your record and ask them what they can do to make that happen. Since this is your first ticket, they may be willing to work with you and you wont even have to go to court. It will only take a phone call or two and maybe a meeting with the DA. Call them and ask...you wont regret it. The worst thing that can happen is they say that they will not bargain with you and then you have to decide if you want to fight it or if you want to just pay for it. No matter what you do end up getting out of this, consider yourself lucky of what you actually got charged for and be thankful that no one got hurt.
