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### Course: 7th grade (Illustrative Mathematics)>Unit 2

Lesson 9: Lesson 11: Interpreting graphs of proportional relationships

# 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
• 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!
• This is so confusing and it makes me very mad
• 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.
• Am i the only one who looks at the comments lol
• no you are not
• Thanks khan you're better than my math teacher
• Poor math teacher XDD
• Y am i doing this
• This is a bit confusing I still don’t get it
• 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

• im having a brain fard
• me too i just want to go home to home honest
• What does K even Mean is it constant of proportionality or what?!!
• 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
• I can understand but at the same time I don't help
• 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.
• what if you ha 0.5 on and 1 on x how would you write that?
• 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)