Berenstein, Carlos A.Lavine, DavidLet L_N be the number of digital line segments of length N that correspond to lines of the form y = ax + BETA, 0 <= a, BETA <=1. In a previous paper [4], a closed form expression for the quantity L_N was obtained. We prove an asymptotic estimate for L_N that might prove useful for many applications. Namely,en-USTechnical Report