When y varies inversely with x, we have a relation like:
[tex]y=\frac{k}{x}[/tex]
where k is a constant.
If we rewrite this relationship, we get:
[tex]k=x\cdot y[/tex]
which means that the product x*y is constant for all pairs of values (x,y) in the function.
Then, if we know that y =15 when x = 4, then we can calculate y when x = 8 as:
[tex]\begin{gathered} (x_1,y_1)=(4,15)_{} \\ (x_2,y_2)=(8,y) \\ x_1\cdot y_1=x_2\cdot y_2 \\ 4\cdot15=8\cdot y \\ 60=8y \\ y=\frac{60}{8} \\ y=7.5 \end{gathered}[/tex]
Answer: y = 7.5
