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# Linear graphs word problems

CCSS.Math:

## Video transcript

what I want to do in 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 in these two axes let's say on the horizontal axis over here I thought the price of a product and let's say in this vertical axis right over here I plot the demand for a product and I'm only plotting the first quadrant here because I'm assuming that 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 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 price were to go up a little bit maybe demand goes down a little bit right price went up a little bit demand went down a little bit if price went up a little bit more maybe demand goes down a little bit more as if price went up a bunch then demand would go down a bunch and so the line that represents the how demand relates to price might look something like this might look something like this and I'm just going to assume for this video that 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 there 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 demand is decreasing now let's think about a different scenario let's imagine that we're talking about the demand for real estate for actual property and let's say that on this axis we plot the population the population in the area and then this is right over here this is demand for demand for land demand for land so when the population is very low you can imagine if the population is zero there's no one there do you even want to buy land so the population is very low the demand is going to be very low and as population increases demand should increase if the population grows a little bit 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 would see a line that looks something like this and once again I drew it as 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 like that or curve that maybe it looks like that we don't know but the general idea is that if someone were to show you a graph that looked like this and said how does as population increases what happens to demand well you'd say look this is population increasing what happens to demand demand is going up here as price increased demand went down here's population is increasing demand went up and you could just make that more general with variables we're talking about specific cases here but if I were to plot something like this if I if you were to see a graph that looked like that looked like that and this is the variable X and this is the variable Y and somewhere to ask you what happens to Y as x increases as x increases well you take any any x that's that's the Y that we're at for that X and as you increase X as you move in the positive horizontal direction as you increase X what's happening to why Y is going up so for this example as x increases Y is increasing Y is increasing if we had a graph that looked like this 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 went like this and you say what happens as a increases as a increases so if you pick it if you pick an A right over here we're at that a and that B right over there as a increases what's happening to B well as a increases our point of the line is now going down B is lower as ba increases here B is decreasing so just want to give you a general idea when X&Y increase together thus the the line goes from the bottom left to the top right we would call this an upward sloping line we would say this has a positive slope when x increases and Y increase when every time x increases Y also increases is upwards sloping positive slope when our independent variable increases and our dependent variable decreases when the independent variable is increasing then you say it has a downward slope or negative slope when we go from the top left to the bottom right