### Proportional relationships (practice) | Khan Academy

Practice telling whether or not the relationship between two quantities is proportional by reasoning CCSS Math: 7. The numbers of left- and right- handed students at West Junior High are proportional to the numbers at East Middle School. Proportional relationships are relationships between two variables where their ratios are equivalent. Identifying the constant of proportionality from equation. Learn all about proportional relationships. How are they Introduction to proportional relationships Identifying the constant of proportionality from equation.

So is this a proportional relationship where the two variables are the cups of milk and the number of eggs? Well, to test that we just have to think about the ratio between these two variables.

### Rates & proportional relationships | 7th grade | Math | Khan Academy

And you can say that the ratio of the number of eggs to the cups of milk, or the ratio of the cups of milk to the number of eggs. But you just need to ensure that they are always equivalent in these scenarios. So let me make another column here, and I'm gonna think about the ratio of the eggs to the cups of milk. Well, in this first scenario one egg for two cups of milk.

This second scenario is three to six. This third scenario is 12 to Are these equivalent ratios?

## For Parents

Well, to go from one to three you multiply by three, and also, to go from two to six, you multiply by three. So you multiplied both the variables by three. Similarly, if you multiply the number of eggs by four, then you multiply the number of cups of milk by four as well. So these indeed are all equivalent ratios, one to two, three to six, 12 to In every scenario you have twice as much cups of milk as you have number of eggs.

So this would be proportional. Now what would be an example of a non-proportional relationship? We'll stay in this baked goods frame of mind. Let's say you're going to a cake store and you're curious about how much it would cost to buy a cake for different numbers of people. So let's say number of servings, number of servings in one column, and then the cost of the cake. And let me set up two columns right over here. Pause this video and see if you can figure out whether this is a proportional relationship.

If it is, why? If it isn't, why not? So let's look at an example of that.

### Eighth Grade / Identifying Examples of Proportional & Non-Proportional Functions

So let's just say that we want to think about the relationship between x and y. And let's say that when x is one, y is three, and then when x is two, y is six. And when x is nine, y is Now this is a proportional relationship.

Because the ratio between y and x is always the same thing.

## Graphing Non-Proportional Linear Relationships

And actually the ratio between y and x or, you could say the ratio between x and y, is always the same thing. So, for example-- if we say the ratio y over x-- this is always equal to-- it could be three over one, which is just three. It could be six over two, which is also just three. It could be 27 over nine, which is also just three. So you see that y over x is always going to be equal to three, or at least in this table right over here.

And so, or at least based on the data points we have just seen. So based on this, it looks like that we have a proportional relationship between y and x. So this one right over here is proportional. So given that, what's an example of relationships that are not proportional. Well those are fairly easy to construct.

So let's say we had-- I'll do it with two different variables. So let's say we have a and b. And let's say when a is one, b is three. And when a is two, b is six. And when a is 10, b is So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when b is three, a is one.