Main content

## Linear models

# Linear graphs word problems

CCSS.Math:

## Video transcript

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 axis, the horizontal axis over here I plot the price of a product and lets say this vertical axis over here i plot the demand for the product, and 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 poeple 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 somplace 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 it 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 is 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 lets 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. We'll you'd say "Look, this is population increasing, what happens to demand?" Demand is going up. Where as 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. Everytime X is increased Y also increases is upwards sloping. When our independant 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.