Question

The pair of points is on the graph of an inverse variation. Find the missing value. (9,5) and (x,6)

Answer 1

(9,5)
Y=k/x
5=k/9 solve for k
K=5*9=45 now use it to solve for the second pair
(X,6)
Y=k/x
6=45/x solve for x
X=45/6==7.5.....answer

Answer 2

The missing value x is,
`(15)/(2)` or
`7(1)/(2)`

Explanation:

The Inverse variation problems can be solved by using the equation, i.e,

`y \propto (1)/(x)`.

use constant variation k to write the above equation as:

`y=(k)/(x)` ......[1]

Now, use the given information to calculate the value of k;

we need to find the value of k ; when x=9 and y=5

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

`k =9* 5`

Simplify:

k =45.

Rewrite the equation [1] by substituting the value of k =45,

⇒
`y = (45)/(x)` ......[2]

Substitute the value y=6 in equation[2] to find x:

`6 =(45)/(x)` or

`x = (45)/(6)` or
`x=(15)/(2)=7(1)/(2)`

Therefore, the missing value x is,
`(15)/(2)=7(1)/(2)`