Graphing in general can be very complicated! In the most general sense it reduces to calculating and plotting a large number of points and hoping they will give you a sense of the actual graph. You entitled this "linear function graphing". You understand, do you not, that a "linear" function is so called because its graph is a straight line? And a straight line is determined by two points. So if y is a linear function of x, choose two convenient values for x, calculate the corresponding values of y, plot those two points, and draw the line between them.