In an inverse variation, the relationship between \( x \) and \( y \) can be expressed as:
\[ y = \frac{k}{x} \]
where \( k \) is the constant of variation.
Given that \( y = 2.5 \) when \( x = 9 \), we can substitute these values into the equation to find \( k \):
\[ 2.5 = \frac{k}{9} \]
To solve for \( k \), multiply both sides of the equation by 9:
\[ k = 2.5 \times 9 \]
Calculating the right side:
\[ k = 22.5 \]
Now that we have found \( k \), we can write the equation for the inverse variation:
\[ y = \frac{22.5}{x} \]
Thus, the constant of variation \( k \) is \( 22.5 \), and the equation for the inverse variation is:
\[ y = \frac{22.5}{x} \]