If there's an inverse variation between x and y then the relation between them can be represented by:
[tex]y=\frac{k}{x}[/tex]
Where k is a constant. Let's see if the table represents an inverse variation. We can start with the first column x=1 and y=60:
[tex]\begin{gathered} 60=\frac{k}{1} \\ k=60 \end{gathered}[/tex]
So according to the first column the relation is:
[tex]y=\frac{60}{x}[/tex]
Let's see if the rest of the table agrees with this. We can take x=2,3,4,5 and 6 and see if the values of y are the same as those in the table:
[tex]\begin{gathered} x=2\colon y=\frac{60}{2}=30 \\ x=3\colon y=\frac{60}{3}=20 \\ x=4\colon y=\frac{60}{4}=15 \\ x=5\colon y=\frac{60}{5}=12 \\ x=6\colon y=\frac{60}{6}=10 \end{gathered}[/tex]
So the y-values given by y=k/x are the ones displays in the table. Then the table represents an inverse variation.
