Transcription
What I want to do with this video is think about the relationship between variables and then think about what the graph of that relationship should look like. So let's say these two axes, the horizontal axis over here, I plot the price of a product, and let's say this vertical axis over here, I plot the demand for the product. I'm only plotting the first quadrant here because I'm assuming that the price can only be positive, and I'm assuming that the demand can only be positive; that people aren't going to pay someone to take the product away from them.
So let's think about what would happen for the price and demand for most normal products. So, if the price is low, you would expect that a lot of people are willing to buy that thing; they're like, "Oh, it's a good price; I would like to buy it." So, if the price is low, then the demand would be high, so maybe it would be someplace over here, all the way that you would have really high demand if the price was zero. So if the price was low, the demand would be high. Now what happens is the price -- so right here the price is low, demand is high; if the price were to go up a little bit, then maybe the demand goes down a little bit, right? Price went up a little bit, demand went down a little bit. If the price went up a little bit more, then maybe demand goes down a little bit more. As the price went up a bunch, then demand would go down a bunch, and so the line that represents how the demand relates to price might look something like this, and I'm just going to assume it's a line. It might not be a line; it might be a curve. It might look something like that. Or it might look something like that.
But in general, if someone were to ask you, if you saw this magenta curve that as price increases, what happens to demand, you just say, "Well, look, price increases; as price increases, what happens to demand?" Well, demand is decreasing.
Now let's think about a different scenario. Let's talk about the demand for real estate, for actual property, and let's say that on this axis that we plot the population, the population in the area, and this right over here, this is demand for land. So when the population is very low, you can imagine, if the population is zero, there is no one there that would want to buy land. So if the population is very low, the demand is going to be very low. And as population increases, demand should increase. If the population increases, more people are going to want to buy land. And if the population goes up a bunch, then a lot of people are going to want to buy land. So you'll see a line that looks something like this. And once again, I drew a line; it doesn't have to be a line; it could be a curve of some kind. It could be a curve that looks something like that, or a curve that looks something like that. We don't know, but the general idea is that if someone showed you a graph that looked like this, and as population increases, what happens to demand, well you'd say, "Look, this is population increasing; what happens to demand?" Demand is going up. Whereas price increased, the demand went down. Here, as population is increasing, demand went up.
And you can just make that more general with variables. We're talking about specific cases here. But if I were to plot something like this, if you were to see a graph that looked like that, and this is the variable x and this is the variable y, and someone were to ask you what happens to y as x increases, well you take any x, that's the y that we have for that x. And as you increase x, as you move in the positive horizontal directions, as you increase x, what is happening to y? Y is going up. So for this example, as x increases, y is increasing. If we had a graph that looked like this, let's call that the a axis and this is the b axis, and maybe our graph looked like this. What happens as A increases? If you pick an A right over here, we're at that A and that B. As A increases, what's happening to B? Well, as A increases, our B is lower. As A increases here, B is decreasing.
So, just wanting to give you a general idea, when X and Y increased together, the line goes from the bottom left to the top right; we would call this an upward sloping line. We would call this a positive slope. Every time X is increased, Y also increases; it is upwards sloping. When our independent variable increases and our dependent variable decreases, when the independent variable is increasing, then you say it has a downward slope, when you go from the top left to the bottom right.