Question

Determine whether set of values represents an inverse variation. If yes, identify the constant of variation and write an inverse variation equation to represent the relationship,

Answer 1

If the table represents an inverse variation, it means that y is inversely proportional to x, written as

`\begin{gathered} y\propto(1)/(x) \\ \propto is\text{ a sign of proportionality } \end{gathered}`

Removing the proportionality sign and introducing a constant k, we have

`\begin{gathered} y=k*(1)/(x) \\ y=(k)/(x) \end{gathered}`

In the first column, we have x = -4 and y = 3.5. Substituting these values for x and y, we have

`\begin{gathered} y=(k)/(x) \\ 3.5=(k)/(-4) \\ k=3.5*-4 \\ k=-14 \end{gathered}`

So, if it's an inverse variation, the relationship would be

`y=(-14)/(x)`

In the second column, x = -2 and y = 7.

Now lets substitute the value of x for -2. If we get y to be 7, then the relationship is an inverse variation

We have

`\begin{gathered} y=(-14)/(x) \\ y=(-14)/(-2) \\ y=7 \end{gathered}`

Since we got y = 7, the relationship is therefore an inverse variation.

The constant k = -14

The equation for the inverse variation is

`y=(-14)/(x)`