Question

The pair of point is on a graph of an inverse variation. Find the missing value.

(9, 5) (x, 6)

A: 45

B: 9

C: 7 1/2

D: 3 1/3

Answer 1

C.
`x=7(1)/(2)`

Explanation:

We have been given a pair of points on a graph of an inverse variation. We are asked to find the missing value for our given point.

We know that when y varies inversely with x, then the equation is:
`y=(k)/(x)`, where, k represents constant of variation.

First of all, we will find constant of variation using point
`(9,5)` as shown below:

`5=(k)/(9)`

`5*9=(k)/(9)*9`

`45=k`

Upon substituting
`k=45` in inversely proportion we will get:

`y=(45)/(x)`

To find the value of x, we will substitute
`y=6` in our equation as:

`6=(45)/(x)`

`x=(45)/(6)`

`x=(15)/(2)`

`x=7(1)/(2)`

Therefore, the missing value is
`7(1)/(2)` and option C is the correct choice.

Answer 2

you have (9,5) & (x,6)

so 9 = k/5

k = 9*5 =45

so 2nd set up have x = 45/6

x = 7.5 = 7 1/2

Answer is C