In an inverse variation, the relationship can be expressed as:
\[ y = \frac{k}{x} \]
Where \( k \) is the constant of variation. To find \( k \), we can use the given values of \( y \) and \( x \).
Given:
- \( y = 2.5 \)
- \( x = 9 \)
We can find \( k \) by rearranging the equation:
\[ k = xy \]
Now we substitute the values:
\[ k = 2.5 \cdot 9 \]
Calculating that gives us:
\[ k = 22.5 \]
Thus, the constant of variation is \( k = 22.5 \).
Now we can write the equation for the inverse variation:
\[ y = \frac{22.5}{x} \]
So, the correct answer is:
k = 22.5; xy = 22.5