By definition, Inverse variation equations have the following form:
[tex]y=\frac{k}{x}[/tex]Where "k" is the Constant of variation.
Given the values shown in the table, you can find the value of "k":
- Choose a point from the table. This could be:
[tex](-3,4)[/tex]Notice that:
[tex]\begin{gathered} x=-3 \\ y=4 \end{gathered}[/tex]- Substitute these values into the equation and solve for "k":
[tex]\begin{gathered} 4=\frac{k}{-3} \\ \\ (4)(-3)=k \\ k=-12 \end{gathered}[/tex]Knowing the Constant of variation, you can write the following equation:
[tex]y=\frac{-12}{x}[/tex]The answer is:
[tex]y=\frac{-12}{x}[/tex]