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when you hear constant of proportionality it can seem a little bit intimidating at first it seems very technical but as we'll see it's a fairly intuitive concept and we'll do several examples and hopefully you'll get a lot more comfortable with it so let's say we're trying to make some type of baked goods maybe it's it's some type of muffin and we know that depending on how many muffins were trying to make that for a given number of eggs we always want twice as many cups of milk so we could say cups of milk cups of milk that's going to be equal to two times the number of eggs so what do you think the constant of proportionality is here sometimes known as the proportionality constant well yes it is going to be two this is a proportional relationship between the cups of milk and the number of eggs the cups of milk are always going to be two times the number of eggs give me the number of eggs I'm going to multiply it by the constant of proportionality to get the cups of milk and we can see how this is a proportional relationship a little bit clearer if we set up a table so if we say number of eggs and if we say cups of milk and make a table here well if you have one egg how many cups of milk you're gonna have well this right over here would be one times two well you're gonna have two cups of milk if you add three eggs well you're going to multiply that by two to get your cups of milk so you're gonna have six cups of milk if you had 1 million eggs so we have a very big party here maybe we're some type of industrial muffin producer well how many cups of milk will you put a million in right over here multiply it by two you get your cups of milk you're going to need two million cups of milk and you can see that this is a proportional relationship to go from number of eggs 2 cups of milk we indeed multiplied by 2 every time that came straight from this equation and you can also see look whenever you multiply your number of eggs by a certain amount you're multiplying your cups of milk by the same amount if I multiply my eggs by a million I'm multiplying my cups of milk by a million so this is clearly a proportional relationship but let's get a little bit more practice identifying the constant of proportionality so let's say I'll make it a little bit more abstract let's say I have some variable a and it is equal to five times some variable B what is the constant of proportionality here pause this video and see if you can figure it out yes it is five give me a B I'm gonna multiply it by five and I can figure out what a needs to be let's do another example if I said that Y is equal to PI times X what is the constant of proportionality here well you give me an X I'm gonna multiply it times a number the number here is PI to give you Y so our constant of proportionality here is PI let's do one more if I were to say that Y is equal to 1/2 times X what is the constant of proportionality pause this video think about it well once again this is just going to be the number that we're multiplying by X to figure out why so it is going to be one half in general you might sometimes see it written like this Y is equal to K times X where K would be some constant that would be our constant of proportionality you see the one half is equal to K here pi is equal to K right over there so hopefully that helps