Question

If y=9 when x=-3, find x when y=6.
Identify the Constant of Variation.

Answer 1

Is this a direct variation or a inverse variation?

Answer 2

direct variation

Answer 3

They are also asking me to determine a solution for the same

Answer 4

Okay so..we have

\[y = kx\]

where 'y' and 'x' we are given and 'k' = constant of variation

so lets plug them in

9 = k(-3)

you want to solve for k..so divide both sides by -3

9 = k(-3)
---------
-3 -3

k = ...?

Answer 5

question. What does that mean and how do I do it? Thank you for your help. I am dense when it comes to this stuff and too old to figure it out on my own....lol

Answer 6

Lol okay no problem

Direct variation can also be stated as " y varies directly as x ," means that when x increases, y increases by the same factor. In other words, y and x always have the same ratio:

The equation to find out the constant of variation in direct variation problems...is written as

\[y = mx\]

Answer 7

I appreciate your help, but what you just said is like me trying to understand a foreign language...lol. I didn't understand this stuff years ago and now I'm trying to help my son and we are both stuck...lol

Answer 8

I think I need a tutor....lol

Answer 9

Well I'm sorry that I cannot explain this better ... I wish I could lol

Answer 10

So would the constant of variation be -2?

Answer 11

The constant of variation in this case would be -3

because "above" 9 / -3

equates to -3

Answer 12

No, you're doing a great job!!! I'm just old and dense when it comes to this stuff...lol
Oh, ok -3. See how dense I am....lol

Answer 13

Okay...so are we on the same page that the constant of variation is -3?

Answer 14

Yes I got that!! Now in the equation you gave me, y=mx. What does the m represent?

Answer 15

Forgive that...as that is a typo

\[y = kx\] is what should be written

Answer 16

'k' not 'm'....and 'k' represents that number we just found...the constant of variation

Answer 17

Oh, ok!!! I have seen that before. Is that what I use to determine the solution?

Answer 18

That is!

We used it before to solve for the constant of variation....but now...we know this value...

It now asks you to find what 'x' equals...when y = 6

\[y = kx\]

This time....we are solving for 'x' rather than 'k' ...so how can you rearrange this formula to solve for 'x'?

Answer 19

find x when y=-3?

Answer 20

No...the second part of your question asks you to solve for 'x' when 'y' = 6

You use that same formula for this...however, now you solve for 'x' rather than 'k' because we KNOW 'k'

\[y = kx\]

since we know 'y' = 6 here....and we found out 'k' = -3...we can plug those in

\[6 = (-3)x\]

so what would 'x' equal?

Answer 21

-2. That's what my calculator said....lol

Answer 22

And that is correct....you would divide both sides by -3

6 = -3x
-------
-3 -3

x = 6 / -3
x = -2

So that is what your answer would be for the second part of your question

Answer 23

Thank you!!! You have been a big help.

Answer 24

No problem and I hope that was understandable!!!

Answer 25

You did a great job explaining!! I am just too dense to absorb all of this at my age. I will be glad when my son is done with this class......lol

Answer 26

*it only gets harder from here lol*

Answer 27

I remember!!! That's why I was glad to be done with school. I was never any good with math..lol