SOLUTION
If the table represents an inverse variation, it means that y is inversely proportional to x, written as
[tex]\begin{gathered} y\propto\frac{1}{x} \\ \propto is\text{ a sign of proportionality } \end{gathered}[/tex]Removing the proportionality sign and introducing a constant k, we have
[tex]\begin{gathered} y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]In the first column, we have x = -4 and y = 3.5. Substituting these values for x and y, we have
[tex]\begin{gathered} y=\frac{k}{x} \\ 3.5=\frac{k}{-4} \\ k=3.5\times-4 \\ k=-14 \end{gathered}[/tex]So, if it's an inverse variation, the relationship would be
[tex]y=\frac{-14}{x}[/tex]In the second column, x = -2 and y = 7.
Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation
We have
[tex]\begin{gathered} y=\frac{-14}{x} \\ y=\frac{-14}{-2} \\ y=7 \end{gathered}[/tex]Since we got y = 7, the relationship is therefore an inverse variation.
The constant k = -14
The equation for the inverse variation is
[tex]y=\frac{-14}{x}[/tex]