Given an Inverse Variation in which "y" varies inversely as "x", you need to remember the form of an Inverse Variation Equation:
[tex]y=\frac{k}{x}[/tex]
Where "k" is the Constant of variation.
In this case, you know that when:
[tex]x=4[/tex]
The value of "y" is:
[tex]y=2[/tex]
Then, you can substitute values into the equation and solve for "k":
[tex]\begin{gathered} 2=\frac{k}{4} \\ \\ 4\cdot2=k \\ k=8 \end{gathered}[/tex]
Therefore, the equation describing the relationship given in the exercise has this form:
[tex]y=\frac{8}{x}[/tex]
Hence, the answer is:
- Equation:
[tex]y=\frac{8}{x}[/tex]
- The numerator is:
[tex]8[/tex]
- The denominator is:
[tex]x[/tex]
