We can think of a linear system as a transformation.
Some information is transformed into some other information.
Buttons and Boxes A shop keeper sells two different types of boxes of buttons. But if the price of buttons changes, the shop keeper will still use the same packages, and still calculate the prices in the same way. But you'll get different prices for the boxes. So he wants a few more points on the graph, so he can easily look up prices. Calculate all the points, and plot them on the graphs, labeling corresponding points with the same number.