Question

y varies inversely as twice x. When x = 2, y = 3. Find y when x = 6

Answer 1

If y varies inversely with 2x, then \[y = \frac{k}{2x}\]where \(k\) is the constant of variation. Plug in your known values to determine the value of \(k\), then use the updated equation to find y when x = 6

Answer 2

i dont know where to even start.

Answer 3

Take my equation. Plug in the values in the "when " statement. Solve for k. Replace k in my equation with the number you got. Plug in the value of x from the "find y when" statement and, well, find y! :-)

Answer 4

do you understand how/why I wrote that equation?

Answer 5

ya hold up im working the problem out

Answer 6

np, I'll get a notification when you respond...

Answer 7

ya i cant figure it out..

Answer 8

okay, we know x=2, y = 3

\[y = \frac{k}{2x}\]\[3=\frac{k}{2*2}\]Solve that for \(k\)

Answer 9

k is the number that when divided by 4 gives you 3. what is k?

Answer 10

dude, are you like growing some extra fingers to work it out, or what?

Answer 11

6?

Answer 12

6 divided by 4 gives you 3?

Answer 13

no buyt my options is 1, 2, 4, or 6

Answer 14

we aren't done yet! we're trying to find k, which you need to find the answer.

Answer 15

you shouldn't need to make any reference to the answer key to work this problem out with 100% certainty.

Answer 16

so, I ask again, what number, divided by 4, equals 3?

Answer 17

12

Answer 18

right! now, we know that k=12, so our equation becomes
\[y = \frac{12}{2x}\]All we have to do to get the answer for the problem is plug in the value of x for which they want to know the value of y.

Answer 19

y=6?

Answer 20

so x=1?

Answer 21

Yes, x = 1. Here's a picture:

Answer 22

You can see that when x=2, y = 3, and when x = 6, y = 1 (y, not x)

Answer 23

and that's the curve shape you get with inverse variation

Answer 24

so the final answer is 1

Answer 25

yes.

Answer 26

thank you.

Answer 27

you're welcome.