We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:
[tex]y=\frac{k}{x}[/tex]
Where "k" is a constant to be determined. To determine "k" we will use the given values:
[tex]\begin{gathered} x=3 \\ y=6 \end{gathered}[/tex]
Now, we plug in the values:
[tex]6=\frac{k}{3}[/tex]
Now, we solve for "k" by multiplying both sides by 3:
[tex]\begin{gathered} 6\times3=\frac{k}{3}\times3 \\ \\ 18=k \end{gathered}[/tex]
Therefore, the value of "k" is 18. Now, we substitute in the relationship:
[tex]y=\frac{18}{x}[/tex]
And thus we get the equation.
