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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 tables

Identifying proportionality constants by looking at tables of values.

## Want to join the conversation?

- Hi! Here is some practice to help you succeed.

Which table has a proportionality of 3?

A

x y

1 2

2 3

3 4

4 5

B

x y

5 15

6 18

7 21

C

x y

1 5

3 15

5 25

Please upvote this so that others can practice too. If there are any problems, please notify me; I a just a learner like you.

Edit- Please do not read the comments until you answer the question. Have a good day!(141 votes)- if I'm allowed to answer its b if not then ill delete this right away(22 votes)

- i hate math. I know that's bad but is it ok even though i work?(16 votes)
- You shouldn't hate math because you think it is hard. Everything is hard when you are learning it. Think about other things you have learned to do that took some time. Believe it or not, math is actually quite easy. If you have the mindset that you are never going to finish something, you never will. You shoulkd stay positive. It's okay to not be perfect at some things, but that doesn't mean that you should give up because it's hard. I like to challenge myself to do things I think is hard. And if we praise students for speed or making things look easy, then the message we are sending them is: I’m only smart when I’m fast or when something is easy. A lot of students say they don’t like math because they are struggling. But you need math to live the rest of your life. If you need help, just ask. That's what Khan Academy was made for.(20 votes)

- How is c not the answer, 2/3 is o.6?(10 votes)
- 2/3 does not equal 0.6

0.6 = 6/10 = 3/5 once reduced.

If you convert 2/3 to a decimal, you will get 0.66666... It is a repeating decimal. You can't truncate the number if you need to maintain the fractions whole value.

Hope this helps.(31 votes)

- Hi! I got a little confused when I went to answer the questions till I figured out a small trick that helped me, especially for the fractions, so I'm going to share it with you guys in hopes it'll help you.

Here's an example, that are like the question you'll do later.*_________*

Which table has a constant of proportionality between y and x of 8/5?

A) X | Y

----------

4 | 32/5

10 | 16

11 | 88/5

For the first row simply type "4 x 8/5 =*_" now do the calculations and figure out the answer. If the answer is the same as the number next to 4 on the table, then that is the correct answer. (If you type this on a calculator it will most likely show you the answer in decimal form, I just converted the decimal number which was 6.4 into a fraction which was 32/5 the number next to 4 on the table.)*and calculate that. If it is again, the same as the beside 10 (which is 16) then you are correct!

Now to be 100% sure, do the same thing for the rest of the numbers on the table.

So write 10 x 8/5 = _

Now for that last one, write 11 x 8/5 =*_ again if it is the same as the number beside 11 on the table (which is 88/5) then you're correct! So A is out correct answer for the whole thing.*

You could also do this even if it's not a fraction.

____________________

B) X | Y

----------

2 | 14/5

6 | 42/5

20 | 28/5

Now, to answer this, do the same thing as shown at the beginning of this.

2 x 8/5 = 3.2 (convert to a fraction which is now 16/5)

We can already tell that 16/5 is not the same as the number beside 2 which is 14/5, not 16/5. So we know from that, that 8/5 is NOT the constant proportionality for this table, so B is not the correct answer to our problem.*____________*

I hope this helped you guys, please upvote if it did, so others can learn from this🔥 🔥 (this whole thing is probably what Sal did in the video but with different words and more confusing💀💀)(19 votes) - May we all get 100% on everything.(15 votes)
- Why doesn't it say that I've finished this? Watched it three times!!(10 votes)
- Did you fast forward the video at all? Sometimes it doesn't count the video if you fast-forwarded it.(11 votes)

- once i watch the videos and then i go to a lesson i cant do it can someone help me😅(11 votes)
- I would watch the videos again and more carefully this time. Focus on equations and key words that Mr. Khan says.(9 votes)

- is there an easy way to do these?(9 votes)
- Yes, there is. If you can divide y/x always to that for every table. If they all have the same answer that means that the table is proportional if not then that means it is non-proportional. I always remember the equation K=y/x(3 votes)

- Why is the constant of proportionality represented as variable “k”. Can it be some other letter? Please help.(4 votes)
- It's really just a convention that everyone uses. Why everyone started using it, I don't know, but you could
**technically**use any other letter.(7 votes)

- This is really easy to understand. Thank you!(10 votes)

## Video transcript

- [Instructor] We are asked, Which table has a constant of proportionality
between y and x of 0.6? Pause this video and see
if you can figure that out. All right, so just as a reminder, the constant of proportionality
between y and x, one way to think about it is that y is equal to
some constant times x. Y is proportional to x. And this constant right over here is our constant of proportionality. So if that's going to be 0.6, so in our tables, or in the table that has a constant of proportionality of 0.6, y should be equal to 0.6 times x for every x,y pair. So let's look at these choices. So is seven 0.6 times four? Well, no, seven is larger than four. 0.6 times four would actually be 2.4, so this one is not gonna be, is definitely not going to have a constant of proportionality of 0.6. And in fact, this table, this isn't even a
proportional relationship. For this first one, I would have to multiply by 7/4. And then here I'm going
to be multiplying by 10/6, which is equivalent to 5/3. And here I'm multiplying by 13/8, so I'm not multiplying by
the same constant every time. So this isn't even a
proportional relationship. Now let's look at choice B. Well, to go from four to 2.4, that is. You would multiply by 0.6. But that's not enough for us to say that this is truly a
proportional relationship. It would have to be 0.6 in every scenario. So let's see. Nine times 0.6, yeah, that is 5.4. Nine times six is 54. But now this is nine times 6/10. It's 54 divided by 10, which is 5.4. And now let's see, 14 times six is 84. So 14 times 6/10 would indeed be 8.4. So this looks like our choice. And we can verify that
this would not be the case. Let's see, three, to get to two we would
be multiplying by 2/3. And then here, once again,
we're multiplying by 2/3. And then here, once again,
we're multiplying by 2/3. So this is actually describing
a proportional relationship, but our constant of
proportionality here is 2/3, which, if you tried to
express it as a decimal, it would be 0.6 repeating. 2/3 is equal to 0.6 repeating. And so it is proportional
but does not have this constant of proportionality. So we like our choice B.