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# Intro to proportional relationships

CCSS.Math:

## Video transcript

what I want to introduce you to in this video is the notion of a proportional relationship and a proportional relationship between two variables is just a relationship where the ratio between the two variables is always going to be the same thing so let's look at an example of that 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 1 Y is 3 and then when X is 2 y is 6 and when X is 9 Y is 27 now this is a proportional relationship why is that because the ratio between y and X is always the same thing 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 3 over 1 which is just 3 it could be 6 over 2 which is also just 3 it could be 27 over 9 which is also just 3 so we see that Y over X Y over X is always going to be equal to 3 or at least in this table right over here and so at least based on the data points we've 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's what's an example of relationships that are not proportional well those are fairly easy to construct so let me let's say we had I'll do it with two different variables so let's say we have a and B a and B now let's say when a is 1 B is 3 and when a is 2 B is 6 and when a is 10 B is 35 so here you might tell me look look what you know when a is 1 B is 3 so the ratio between for the ratio B to a you could say B to it's you could say well us when when B is 3 a is 1 or when a is 1 B is 3 so 3 2 1 and that's also the case when B is 6 a is 2 or when a is 2 B is 6 so it's 6 2 2 so these ratios seem to be the same they're both 3 but then all of a sudden the ratio is different right over here this is not equal to 35 over 10 this is not equal to 35 over 10 so this is not a proportional relationship in order to be proportional the ratio between the two variables always has to be the same so this right over here this is not not not proportional not proportional so the key in identifying a proportional relationship is look at the different values that the variables take on when one variable is one value and then D and then what does the other variable become and then take the ratio between them here we took the ratio Y to X and you see Y to X or Y divided by X the ratio of Y to X is always going to be the same here so this is proportional and you could actually gone the other way you could have said well what's the ratio of X to Y X to Y well over here would be 1 2 3 1 2 3 which is the same thing as 2 2 6 which is the same thing as 9 2 27 nine to 27 when you take this ratio between few say the ratio of X to Y instead of Y to X you see that it's always 1/3 but anyway you look at it the ratio between these two variables if you say Y to X it's always going to be 3 or X to Y is always going to be 1/3 so this is proportional while this one is not