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Identifying the constant of proportionality from equation

Understanding what a constant of proportionality is and how to identify it in an equation.

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  • winston baby style avatar for user Brian
    who invented math
    (62 votes)
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  • leaf green style avatar for user Brajendra Singh
    When Sal used the example y=kx. Does the constant of proportionality always have to be the first variable?
    (8 votes)
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    • piceratops ultimate style avatar for user Frodo Baggins
      Well, in your example, y = kx, the constant of proportionality (k) is not the first variable. Anyway, no, the constant of proportionality does not have to be the first variable. You can write y = kx and kx = y and it means the same thing.

      Hope this helps! :)

      Edit: Also, y=xk and y=kx are the same thing
      (19 votes)
  • blobby green style avatar for user BabyGirl
    This is so hard for me i cant believe i made to 8th grade!
    (13 votes)
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  • starky tree style avatar for user Hortência
    can the constant of proportionality be pi?
    (4 votes)
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  • duskpin ultimate style avatar for user kaungkhantwin3003
    What is pi?
    How to use pi?
    (6 votes)
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    • hopper cool style avatar for user Philip
      The constant pi is the value of the ratio between the circumference of a circle to its respective diameter. Pi is used to help calculate approximate values of a circle's circumference or arc length, radius, diameter, or area when you have other known values of a circle.

      Here are some of the formulas for circles (the symbol π means pi)
      Area= π × r^2 [Pi times radius squared]
      Circumference = 2 × π × r [2 times pi times radius; the diameter is twice the radius]
      Circles are different from polygons, such as triangles, quadrilaterals (e.g. squares and rectangles), because they are "curvy" and thus require a somewhat different method of calculation, and is why we need pi for better accuracy, instead of just some "base times height".
      In 3-D geometry, some "solids" that have a circle as part of the structure are cylinders, cones, and spheres; so to find the surface area or volume for those, pi will be necessary.
      Cylinder: volume = π×r^2 h [pi times radius squared times height]
      Cone:volume=(1/3) × π × r^2 × h [pi times radius squared times height, all over 3]
      Sphere:volume= (4/3) π r^3 [four-thirds times pi times radius cubed]
      (6 votes)
  • starky sapling style avatar for user Loading...
    I heard if a table is proportional, it will cross the origin on a graph. Is that true?
    (6 votes)
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  • hopper cool style avatar for user Bryant Hu
    Can you reverse the constant rate of proportionality? Like say y=5x then you multiply 5 and get y but can you divide y by 5 and get x?
    (5 votes)
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  • mr pink green style avatar for user Makayla Ruby
    i do not get it?
    (4 votes)
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  • stelly orange style avatar for user Christian Alcala
    Hi! Here is some practice to help you succeed!

    Find the constant of proportionality in this table. I know the table is a bit off, I apoligize for that. This is just the way Khan Academy formats it.

    Scoops Cones


    2 30

    3 45

    4 60


    Please upvote this so everyone can practice. If there is any problem with the question, tell me. I am a learner too!

    Edit- Please refrain from reading the comments below until you have solved the problem. If you need help I will be more than happy to answer your questions.
    (4 votes)
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  • blobby green style avatar for user Kirill Dmitriev
    I get it that if we have equation y = kx, then k is the constant of proportionality. What if the equation is y = kx + b, where b is some other constant? Would k still be called constant of proportionality in that case?
    (3 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      For y = kx + b with b nonzero, we would have a linear but non-proportional relationship. In this situation, k is not a proportionality constant.

      However, k is the rate of change, also called the slope, whether or not b is zero.

      Have a blessed, wonderful day!
      (2 votes)

Video transcript

- [Instructor] 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 some type of muffin, and we know that depending on how many muffins we're 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 are you gonna have? Well this right over here would be one times two, well you're gonna have two cups of milk. If you had three eggs, well you're just gonna multiply that by two to get your cups of milk, so you're gonna have six cups of milk. If you had 1,000,000 eggs, so we have a very big party here, maybe we're some sort of industrial muffin producer, well how many cups of milk? Well you put 1,000,000 in right over here, multiply it by two, you get your cups of milk. You're going to need 2,000,000 cups of milk. And you can see that this is a proportional relationship. To go from number of eggs to cups of milk, we indeed multiplied by two every time. That came straight from this equation. And you could 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 1,000,000, I'm multiplying my cups of milk by 1,000,000. So this is clearly a proportional relationship. 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 y. So it is going to be 1/2. 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 1/2 is equal to k here, pi is equal to k right over there. So hopefully that helps.