1. A tennis line-calling system that makes line calls for a plurality of tennis players striking a tennis ball with their respective tennis racquets, causing the tennis ball to move across each side of a tennis court, comprising: (a) an integrated tennis line-calling device that includes: (i) a camera system that generates successive video frames covering court lines of the tennis court and the tennis ball as it moves across each side of the tennis court; and (ii) a line call analyzer that: (A) processes the video frames in real time, (B) determines when the tennis ball bounces on the playing surface of the tennis court based upon the processing of the video frames, (C) determines the location of the tennis ball upon its initial bounce relative to the location of one or more of the court lines of the tennis court, and (D) makes a line call based upon the relative location of the tennis ball upon its initial bounce and the one or more court lines of the tennis court; and (b) an attachment mechanism that enables the integrated tennis line-calling device to be attached to or in proximity to a net post of a tennis court.