 An important skill in all of mathematics is to understand sign and magnitude, whether something is positive or negative, and whether it is a large number or a small number. And this is particularly true when graphing. And part of the reason for that is that graph is a way of organizing information, but it is not something that we will ever successfully use in a mathematical argument. It helps organize the data, it helps us guide our thinking, but the actual process of solution is almost always going to be based on some sort of algebraic manipulation. And because of that, the thing that helps organize our thoughts more than anything else is going to be sign first and magnitude a little bit later on. And magnitude, we could really mean relative magnitude here. So, for example, let's take negative 1. Well, this is a small number, relatively speaking. It's a small number, but it's also negative. So negative 1 is a small negative number. Likewise, 30,195, that is a large number that happens to also be positive. And what does that mean? Well, let's say I have to graph the point negative 1, 30,195. So one way I could graph it is I could read this literally. I start at the origin. I go back one unit. There's my x-coordinate. I go up 30,195 units. So I'm going to go up 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14. And after a couple of weeks, I'll get to the correct point. But the other way I can look at it is negative 1, well, slightly to the left of the origin. Large positive number way above the origin. I'm up here someplace. As a general rule, sign is more important than magnitude. And relative magnitude is more important than the absolute magnitude. We'll see what that means in a second. So, for example, let's say I want to sketch on the same graph a whole bunch of points, negative 5,400, 25,1,30, 11,5, negative 13, negative 17. So my first point A has coordinates negative 5,400. So how do I graph that? I could throw down my axes, and then let's see the coordinates A. I'm going to go back 5, 1, 2, 3, 4, 5, and I'm going to go up 400. I'm going to go up 400 units. I'll count 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. And after a couple of minutes, I'll get to 400. More efficiently, the thing I will note are sign and magnitude. So the x-coordinate is negative. So that tells me I'm to the left of the origin. The y-coordinate is positive. So I'm above the axis. And 400, especially in comparison to 5, 400 is a large number. So not only am I above the axis, but I'm very far above the axis. So my quick sketch of that location has something like this. So I'm back some distance, a small distance, and I'm up a very large distance. And so there's a rough sketch of where the point negative 5,400 is going to be. Well, what about the other point? 25, 1, 3, negative 11, 5. Well, we'll run the same sort of sign and magnitude analysis. So the x-coordinate is positive. So I'm going to be someplace to the right of the axis. The y-coordinate is negative. So I'm going to be below the x-axis. And again, relatively speaking, our x-coordinate is large. Our y-coordinate is small. This is 25 in change. This is negative 11 fifths, around 2. So the x-coordinate is much larger than the y-coordinate. So I'm going to be over a fair distance, but down just a small distance. So I should graph our point accordingly, located there someplace. And finally, our third point C, negative 13, negative 17. So sign is more important. Sign is negative x-coordinate. So I'm to the left of the origin. The y-coordinate also negative. So I'm going to be below the origin. So I'm going to be over here someplace. And here we may want to make a comparison. We do have some other points that we've graphed. And the more points you graph, the more you want to make sure that your new points are consistent with the previous points. So this point A was 5 units to the left of the origin. I want to be negative 13 units from the origin. I want to be farther to the left than I was at A. So I'm going to be farther to the left. Also, my B-coordinate, I went down a small amount. I'm going to go down farther to get to C. So I want to be farther over than I was at A, farther down than I was at B, and I'm going to plot C roughly there.