The Solution.
Step 1:
We shall write out the general equation that defines the inverse variation between y and x.
[tex]\begin{gathered} y\propto\frac{1}{x} \\ \\ \Rightarrow y=\frac{1}{x}\times k \\ \\ y=\frac{k}{x} \end{gathered}[/tex]Step 2:
We shall substitute 4 for y, and 8 for x in the above equation, in order to get the value of k.
[tex]\begin{gathered} 4=\frac{k}{8} \\ \text{Cross multiplying, we get} \\ k=4\times8 \\ k=32 \end{gathered}[/tex]Step 3:
Presentation of the Answer.
The inverse variation between y and x is defined by the equation below:
[tex]y=\frac{32}{x}[/tex]Therefore, the correct answer is
[tex]y=\frac{32}{x}[/tex]
