Constant of proportionality in both directions
About this video
Rosie's pasta graph shows a proportional relationship: 4 eggs per liter of flour, so E = 4F and the constant of proportionality is 4. Going the other way, she uses 1/4 liter of flour per egg, the reciprocal of 4.
You'll be able to
- read the constant of proportionality from a graph through the origin.
- write an equation like E = 4F for a proportional relationship.
- find the constant of proportionality in the other direction as the reciprocal.
Key words
- proportional relationship
- A relationship whose graph is a straight line through (0, 0), so one quantity is always a constant times the other.
- constant of proportionality
- The number of one quantity per one unit of the other, like 4 eggs per liter.
- reciprocal
- The number you multiply by to get 1; the reciprocal of 4 is 1/4.
Transcript
- [Instructor] We are told Rosie is mixing flour and eggs to make pasta. The graph shows how many eggs she uses for different amounts of flour. Okay, I see that. How many eggs does Rosie use per liter of flour? Pause this video, have a go at this. Okay. So it looks like a proportional relationship if Rosie is not using any flour than producing zero or using zero eggs.
And then it looks like the slope here is four. For every extra flour, Rosie is using four extra eggs. So how many eggs does Rosie use per liter of flour? I like that being four. You could really think of this as the constant of proportionality. If we said that eggs is equal to four times the amount of flour in liters, then you could see if you divide both sides by F, you get eggs divided by flour is equal to four.
Or you could say that this takes the form E, eggs is equal to the constant of proportionality times flour where our constant proportionality right over here is four. How many liters of flour does Rosie use per egg, per egg? Okay, so let's think about this very carefully.
If we're using four eggs per liter of flour, so four eggs... Another way to think about this is if we're thinking four eggs per one liter of flour, this is trying to go the other way around. This is liters per egg. So go the other way around, one liter for every four eggs.
Or another way to think about it, this is one fourth of a liter per egg. So the answer right over here is one fourth.
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