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

Answer:

The missing value x is, $\frac{15}{2}$ or $7\frac{1}{2}$

Step-by-step explanation:

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

$y \propto \frac{1}{x}$.

use constant variation k to write the above equation as:

$y=\frac{k}{x}$                         ......[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

$5=\frac{k}{9}$ or

$k =9\times 5$

Simplify:

k =45.

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

⇒ $y = \frac{45}{x}$                     ......[2]

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

$6 =\frac{45}{x}$ or

$x = \frac{45}{6}$ or $x=\frac{15}{2}=7\frac{1}{2}$

Therefore, the missing value x is, $\frac{15}{2}=7\frac{1}{2}$