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## 7th grade (Illustrative Mathematics)

### Unit 2: Lesson 9

Lesson 11: Interpreting graphs of proportional relationships# Constant of proportionality from graph

Sal finds constant of proportionality by looking at the graph of a line.

## Want to join the conversation?

- I'm confused in the constant proportionality and the way you set it up(25 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!(22 votes)

- This is so confusing and it makes me very mad(23 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.(7 votes)

- Am i the only one who looks at the comments lol(17 votes)
- why is school so boring(8 votes)
- it’s because its a feature for the matrix(5 votes)

- Thanks khan you're better than my math teacher(7 votes)
- This is a bit confusing I still don’t get it(3 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!(7 votes)

- what if you ha 0.5 on and 1 on x how would you write that?(4 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!(5 votes)

- when can there be no propotion(4 votes)
- There is no proportion when x and y are interacting together.

For example, when you have a proportion like y=x+2, you will have a straight line on the graph. But when you have something like y=xy, you will get a curved line on the graph which does not fulfill the rule that a proportional relationship should be graphed as a line.(4 votes)

- But what if you have a decimal, then how do you apply this method?(5 votes)
- You can divide the decimals. In a proportional relationship (line through the origin), the proportionality constant is y/x for any chosen point (x,y) on the graph with x nonzero.(2 votes)

- what 3/2 Constant of proportionality from graph(3 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.