Question

23. Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.

x 8 11 14 17
y 1 10 18 31

Answer 1

I got inverse varation; y=8/x
am i right?

Answer 2

@Math4Life
\(y=\frac{8}{x}\) is satisfying only the first one. You see when x=11 y=10 and as x increases y is also increasing so it's not an inverse relation. Let's check if it's a direct relation

Answer 3

direct varitation, y=1/8x ?

Answer 4

Let's have the relation
y=mx+c
We'll use first two data and try to find m and c
And then we'll check if it satisfies the others

Answer 5

if it's not " direct variation, y=1/8x then it has to be neither

Answer 6

From first we have x=8, y=1
so
\[1=8m+c........................................(1)\]
from second we have, x=11, y=10
\[10=11m+c..................................... (2)\]
Let's subtract 1 from 2, we get
\[10-1=11m+c-(8m+c)\]
We get
\[9=3m\]
so
\[m=3\]
now we need to find c
\[1=8m+c\]
m=3
\[1=24+c\]
so
\[c=-23
\]
so the relation is
\[y=3x-23\]
now let's check if it satisfies the other points

Answer 7

ok please continue, thank you this is a really big help!

Answer 8

Third x=14 and y=18. Let's check if it satisfies
Our proposed relation
\[y=3x-23\]
x=14
\[y=3\times 14-23= 18\]
Wow this one satisfied this. I've a feeling that this is our relation:D:D
But we have to check others also

Answer 9

Fourth
x=17 y=31
\[y=3x-23\]
x=17
\[y=3 \times 17-23\]
\[y=51-23=28 \ne 31\]
oh no:(:(
This relation failed for this
Unfortunately there is no relation between x and y.
It's neither:(

Answer 10

@ash2326 thank you so much! with showing your work i really understood it! thanks! now this is my first question so what do i do after you answer? do i give u a grade or points or something?

Answer 11

You thanked me. That's enough. Welcome to Open Study:D
I'm glad to help you:D:D

Answer 12

if you dont see a "good answer" button next to ashes name; hit f5 to refresh your browser and see if it appears.

the thank you is sufficient tho; but the medals are that little extra :)

Answer 13

@Math4Life One important thing. Here at Open Study We have a code of conduct. Always follow it and you'd be a nice user.
Here is the link to that http://openstudy.com/code-of-conduct
Read it through
Thanks

Answer 14

@amistre64 I think this user left. Could you please close this question?

Answer 15

@ash2326 Was I not being a nice user?

Answer 16

You are a nice user. I think you won't have any problem following the code of conduct.:D

Answer 17

@ash2326 Ok thanks! Well i'm going to close the question, thank you!

Answer 18

Great:D:D