Answer
The variation constant is 108
The equation of variation is y = 108/x
Explanation
y varies inversely to x implies:
[tex]y\propto\frac{1}{x}[/tex]So, introducing a constant, we have
[tex]\begin{gathered} y=k.\frac{1}{x} \\ y=\frac{k}{x}----a \end{gathered}[/tex]Substitute y = 12 and x = 9 into (a)
[tex]\begin{gathered} 12=\frac{k}{9} \\ k=12\times9 \\ k=108 \end{gathered}[/tex]Therefore the variation constant = 108
To find the equation of variation, substitute k = 108 into (a)
[tex]\begin{gathered} \text{Recall (a)} \\ y=\frac{k}{x} \\ \therefore\text{ The equation of variation is }y=\frac{108}{x} \end{gathered}[/tex]