Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive $ y $ direction) for $ 10 $ units. Then she turns east (the positive $ x $ direction) and as she's turning her camera flies out the window and lands exactly at $ (0,10) $. She then drives $ 9 $ units east, turns and drives $ 8 $ units north. She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving $ 1 $ unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as $ ax+by=c $, where $ a $, $ b $, and $ c $ are integers, $ a>0 $, and $ a $ is as small as possible.