Given the information on the table, we can find out the constant of variation by working a few cases:
[tex]\begin{gathered} k=\frac{y}{x} \\ \Rightarrow k_1=\frac{-8}{-2}=4 \\ k_2=\frac{-16}{-4}=4 \\ k_3=\frac{-24}{-6}=4 \end{gathered}[/tex]
Therefore, k=4. To find the equation we simply solve for y the first equation:
[tex]\begin{gathered} k=\frac{y}{x} \\ k=4 \\ \Rightarrow4=\frac{y}{x} \\ \Rightarrow4x=y \end{gathered}[/tex]
Finally, the equation is y=4x
