I think someone mentioned in lecture that we should color in pixels in varying shades depending on how much of it was intersected by the line, and this behavior definitely shows up when compressing images-- what algorithms are used when computing what color to make a pixel in a compressed image (I'm guessing some kind of averaging)?

I think during this lecture there was a focus on direct rasterization and not any anti-aliasing techniques to help improve the rasterization. I am making an educated guess that when implementing rasterization it can be hazardous to pre-emptively design it around anti-aliasing because in certain cases you might want a direct representation of the image.