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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,

Determine whether set of values represents an inverse variation. If yes, identify-example-1
User Geremy
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1 Answer

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SOLUTION

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)

User Stefan Teitge
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