It is given that z varies directly with x and inversely with y.
[tex]z=\frac{kx}{y}[/tex]
Where k is the constant of proportionality.
First, let us find the value of constant (k).
Substitute x = 6, y = 2, and z = 15
[tex]\begin{gathered} 15=\frac{k\cdot6}{2} \\ k\cdot6=2\cdot15 \\ k\cdot6=30 \\ k=\frac{30}{6} \\ k=5 \end{gathered}[/tex]
So, the value of k is 5
[tex]z=\frac{5\cdot x}{y}[/tex]
Finally, let us find the value of z when x = 4 and y = 9
[tex]\begin{gathered} z=\frac{5\cdot4}{9} \\ z=\frac{20}{9} \end{gathered}[/tex]
Therefore, the value of z is 20/9
