Given,
z is directly proportional to the product of x and y.
The value of z is 15 when x is 5 an y is 6.
According to the question,
[tex]\begin{gathered} z\propto x\times y \\ z=\text{kxy} \end{gathered}[/tex]
Here, k is proportionality constant.
Substituting the value of x, y and z then,
[tex]\begin{gathered} 15=k\times5\times6 \\ 15=30k \\ k=\frac{1}{2} \end{gathered}[/tex]
Susbtituting the value of k in the above expression then,
[tex]z=\frac{1}{2}xy[/tex]
Hence, the equation that shows the relation of x, y and z is z=1/2xy.
