Question

Need to know if do the tables of values represent inverse variation. number 15

Answer 1

If there's an inverse variation between x and y then the relation between them can be represented by:

`y=(k)/(x)`

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:

`\begin{gathered} 60=(k)/(1) \\ k=60 \end{gathered}`

So according to the first column the relation is:

`y=(60)/(x)`

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:

`\begin{gathered} x=2\colon y=(60)/(2)=30 \\ x=3\colon y=(60)/(3)=20 \\ x=4\colon y=(60)/(4)=15 \\ x=5\colon y=(60)/(5)=12 \\ x=6\colon y=(60)/(6)=10 \end{gathered}`

So the y-values given by y=k/x are the ones displays in the table. Then the table represents an inverse variation.