Question

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

(5, 4) and (x , 7)


5








20

Answer 1

In an inverse variation, the product of the two variables remains constant. This means we can express it as \( x \times y = k \), where \( k \) is a constant.

From the given point \((5, 4)\), we can calculate \( k \):

\[
k = 5 \times 4 = 20
\]

Now we have the constant \( k = 20 \).

Now we use the other point \((x, 7)\):

\[
x \times 7 = 20
\]

To find \( x \), we can rearrange this equation:

\[
x = \frac{20}{7}
\]

Thus, the missing value \( x \) is \(\frac{20}{7}\).

If you want the decimal approximation or additional detail, \( \frac{20}{7} \approx 2.857 \).