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### Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 2: Constant of proportionality- Introduction to proportional relationships
- Identifying constant of proportionality graphically
- Constant of proportionality from graph
- Constant of proportionality from graphs
- Identifying the constant of proportionality from equation
- Constant of proportionality from equation
- Constant of proportionality from equations
- Constant of proportionality from tables
- Constant of proportionality from tables
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)

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# Constant of proportionality from graph

In this lesson, we learn about the constant of proportionality in a graph. It's the number we multiply by x to get y. In our example, when x increases, y increases three times as much. So, our constant of proportionality is 3.

## Want to join the conversation?

- I'm confused in the constant proportionality and the way you set it up(35 votes)
- The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

Hope this helps!(48 votes)

- This is so confusing and it makes me very mad(44 votes)
- Hey, don't worry. Everyone has their least favorite subjects. If you look at the comment above, they explain how to find it. There is also another equation, but thats for later.(21 votes)

- Am i the only one who looks at the comments lol(34 votes)
- no you are not(12 votes)

- Thanks khan you're better than my math teacher(23 votes)
- Poor math teacher XDD(2 votes)

- Y am i doing this(15 votes)
- This is a bit confusing I still don’t get it(8 votes)
- So, Y (the up and down part of the graph) equals K (The constant of proportionality, you get it by dividing Y by X), times X (the side by side part of the graph.)

This would equal= Y=KX

Then you look for a clear place where you can place a point, (I would recommend using graph paper for this) say, (4,8) and then you take the Y (X,Y) which is 8 and divide it by the X, which is 4 to get 2.

So, K=2.

Now lets check it.

8=2(4)

8=8

I hope this was helpful!(15 votes)

- im having a brain fard(11 votes)
- me too i just want to go home to home honest(5 votes)

- What does K even Mean is it constant of proportionality or what?!!(9 votes)
- K is in fact the constant of proportionality.

If you have a graph of a proportional relationship, you can pick any point on the graph (x,y) and k will equal y/x(4 votes)

- I can understand but at the same time I don't help(8 votes)
- Ok so basically your y value will always be doubled from your x value or even sometimes tripled but the main reason for that is so that you can get an even number so you can multiply the x value and see how much the y value is. Therefore, say you have 2 and 4 you have to multiply 2 two times to get 4. So our formula is y=kx meaning that you should use that formula to solve that answer. In conclusion, y=2x.

Hope this helped you understand your proportionalities.(6 votes)

- what if you ha 0.5 on and 1 on x how would you write that?(5 votes)
- If 0.5=Y, 1=X.

This is going to get a bit confusing, but I will say, I typically prefer more cleaner numbers. (On graph paper)

0.5=K1

0.5/1=K

0.5=K. (you divided 0.5/1)

Now lets add it back in to see if we're correct.

0.5=0.5(1)

0.5=0.5 (you times 0.5*1)

I hope this was helpful!(8 votes)

## Video transcript

- [Instructor] The following graph shows a proportional relationship. What is the constant of proportionality between y and x in the graph? Pause this video, and see
if you can figure that out. All right, now let's do this together, and let's remind ourselves what a constant of
proportionality even is. If we know that there is a
proportional relationship between y and x, then
there will be a constant of proportionality
between these variables, and what this is, is it is a number that I would have to
multiply x by to get to y. So I could make a little table here, as we often do when we describe
proportional relationships, x and y. We know that when x is zero, y is zero. But if I multiply zero by
anything, I'm gonna get zero. But then when x is one, what is y? When x is one, y is three. They mark it right over there. When x is two, what is y? X is two, we see that y is six. So our constant of proportionality is what are we multiplying x by to get to y? Well, let's see, to go from one to three, I have to multiply by three. To go from two to six, I
have to multiply by three. Another way to think about it is we could write the equation y is equal to something times x. The number that we multiply x by to get y is our constant of proportionality. And we've seen, in all
of these situations, this should be true for
any point on this line. You give the x, you multiply
it by three, you get your y. So the relationship here
is y is equal to three x. So three is our constant
of proportionality.