Main content

## 8th grade

### Course: 8th grade > Unit 3

Lesson 9: Linear models- Linear graphs word problems
- Modeling with tables, equations, and graphs
- Linear graphs word problem: cats
- Linear equations word problems: volcano
- Linear equations word problems: earnings
- Modeling with linear equations: snow
- Linear equations word problems: graphs
- Linear equations word problems
- Linear function example: spending money
- Linear models word problems
- Fitting a line to data

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Linear graphs word problems

Sal discusses how we would go about making sense of the direction of a linear graph that represents a relationship between two real-world quantities. Created by Sal Khan.

## Want to join the conversation?

- if there was a third dimension would it be labeled z?(55 votes)
- Yes. It is labeled z. You can use it to plot three dimensional figures, such as cubes and pyramids, if you connect the dots. As for lines in the third dimension, you can have one independent variable and two dependent ones. With it.(52 votes)

- Why are some lines curved and some are straight?(21 votes)
- It really depends on the x and y values. So for example, a cup with a large bottom and thin top would have a curve on its graph of time and liquid(23 votes)

- What would a non linear graph look like?(3 votes)
- Non-linear graphs can refer to any other equations that can be graphed on a coordinate plane that are not in linear form:
`y=mx+b`

Normally, this means that it will be a large**polynomial equation**.

With differently sized exponents per term, the graph can be manipulated into fantastic shapes and curves that are definitely not linear.

This is a good site to play around with that--

https://www.desmos.com/calculator(16 votes)

- Can a discrete graph also be continuous?(9 votes)
- hmm... I'm not QUITE sure if it can, probably not because

Continuous graphs represent functions that are continuous along their entire domain. These functions may be evaluated at any point along the number line where the function is defined. For example, the quadratic function is defined for all real numbers and may be evaluated in any positive or negative number or ratio thereof. Continuous graphs do not possess any singularities, removable or otherwise, in their domain, and possess limits across their entire representation.Discrete graphs represent values at specific points along the number line. The most common discrete graphs are those that represent sequences and series. These graphs do not possess a smooth continuous line but rather only plot points above consecutive integer values. Values that are not whole numbers are not represented on these graphs. The sequences and series that produce these graphs are used to analytically approximate continuous functions to any desired degree of accuracy.(6 votes)

- couldnt demand be negative(3 votes)
- I don't think it can.

Demand means that people want something so naturally the higher the demand for something, the higher the price gets. The lower the demand the lower the price.

But think about if demand were negative, it would mean that instead of a paying a price for getting something, you get paid instead.(9 votes)

- Why are there letters?(5 votes)
- IF you are asking on graphs, they are there usually so you can identify them so later in the problem if they ask you

A. What is (5,5)

You can answer the letter S if S is at where (5,5) is.

Or

B. B (8,9)

You can put B on the place where (8,9) is.(5 votes)

- Is there a 3rd and 4th dimension in graphs? If so, then what would it be labeled?(4 votes)
- Yes, but I wouldn't worry about that for now. Instead, get really good at working with just two dimensions. That way, when you get to three dimensions and more, you'll have a solid foundation to build on.(4 votes)

- In the problem shown in3:14up to3:54when he said x increases then y increases what does Sal mean by that?(4 votes)
- what the heck is this guy saying when he says demand(3 votes)
- The demand is how many people want to buy the product.(5 votes)

- Can there be more than 3 dimensions or just three.(4 votes)

## 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.