How do I get out of a " failure to avoid a accident " case in court ?

I have a court date set for next week , I'm being charged with failure to maintain a safe speed in order to avoid an accident , or something along those lines . I sharply swerved to the right in an attempt to avoid a car tht was drifting into my lane and consequently dinged my car against the guard rail . The car never stopped and 4hrs later 3 troopers arrive and hand me a ticket. Also , just a side note, the trooper had called one if there contract towing companies even tho I told him that my insurance had already dispatched a tow truck driver , was that leagal ? Or fair practice ? Getting back to the subject at hand ; due to the nature of my job , I am required to have a clean record , how can I avoid picking up this bill , and get this case dismissed ? Thanks