 Okay, this is Professor Gerald Friedman, University of Massachusetts Amherst, and we're going to talk about graphs and graphing. In the beginning of my classes, the first day, I usually have the students fill out a little form saying something exciting about themselves, something that they hope to learn in the class, and something that concerns them. I could skip the last question these days because I know what concerns them. Well, first, they're concerned about the 8 a.m. start time of my brick-and-mortar class. They hate that, so do I, all agreed. Second, they're worried about math. Why do people worry so much about math? I could argue with you, as I do myself, oh, come on, we don't use math, and most we use arithmetic, maybe a little bit of arithmetic, adding and subtracting. We don't use, we don't do real graphs. We just do really simple things. But the fact is that people worry about these, worry about this. So I want to talk a little bit about graphs, and I want to make it clear that this is not something to worry about. It's actually what we use for this class, for Econ 103, Introduction to Microeconomics. It's very simple, arithmetic and graphs. Simple and also useful. It all starts with a table of numbers. For example, hours studying and grades. Zero, you get 10% right. Be warned, you need to study for this class. One hour, maybe you get 20% right. Two hours, 30, three hours, 40. You see where this is going. So dot, dot, dot, dot, dot, dot, okay. So all there is, nothing more complicated. Two dimensions, a simple table of numbers with two types of numbers. There's an equation here if you're interested. The equation is grades equals 10 plus 10 times hours. So if hours is zero, your grade is 10. If hours is one, your grade is 10 plus 10. That's it, that's it. It's hardly math, just arithmetic. Now, we make from this a graph, a simple graph. And the graph has two dimensions because they're two numbers. Down here, we have hours studying. We put this on the bottom, on the horizontal axis. And if you don't want to learn the word, don't worry about it, it doesn't matter. We put it on the bottom. The hours studying, we put that on the bottom because that's what you control. You control how many hours you study. You may say, oh, I don't control it because I need to eat pizza and I need to go out listening to music and dance and whatever, but you control how many hours you study. The outcome is what's up here, which is the product of what you control. You control this and you get the grade. And it's going to look something like that. The more you study, the higher your grades. And there's a straight line, what you can call a linear relationship, but you don't need to call it that. It's just this is the product of that. More studying, higher grades. You learn from this that the relationship is positive, higher grades come from more studying. And you learn from this that your conclusion, that you'll get a higher grade if you're studying, is represented by the graph. It's represented by the numbers in the table, but it's all made up. Is it true? I don't know. You could do a study, you could investigate, you could ask all your friends how many hours do you study, what grades did you get, et cetera. But your graph here is not a fact. It's an assumption. And all you're doing with this arithmetic and this graph is putting out there, externalizing your view of the world. Your worldview is represented here. Your view of how you get higher grades. Or in this case, my worldview is represented here, that you'll get higher grades if you study. And you'll get higher grades if you relax about the math and the graphs. You can do it. If you got this far in life, I am completely confident that you can handle simple graphs and numbers. Okay, thank you very much and have a good day.