Question

6.
The pair of points is on the graph of an inverse variation. Find the missing value.

(9, 5) and (x , 6)

Answer 1

In inverse variation, the product of the two variables is constant. This can be represented by the equation:

\[
xy = k
\]

where \( k \) is a constant.

Given the points (9, 5) and (x, 6), we can calculate \( k \) using the first point (9, 5):

\[
k = 9 \cdot 5 = 45
\]

Now we can use the second point (x, 6) to find \( x \):

\[
x \cdot 6 = 45
\]

To solve for \( x \), divide both sides by 6:

\[
x = \frac{45}{6} = 7.5
\]

Thus, the missing value is:

\[
\boxed{7.5}
\]