The document derives Bresenham's line algorithm for drawing lines on a discrete grid. It starts with the line equation and defines variables for the slope and intercept. It then calculates the distance d1 and d2 from the line to two possible pixel locations and shows that the sign of d1-d2 determines which pixel to plot. The derivation continues by multiplying d1-d2 by the change in x to obtain an integer parameter pi, which is then defined recursively to form the core of the algorithm using only integer calculations. Initial and increment values for pi are also derived. Finally, pseudocode is provided to outline the complete algorithm.