Chapter 11, Problem 2PT

To determine

To find: Determine whether each table represents an inverse variation.

Answer to Problem 2PT

The table of values represents the inverse variation is $xy=4$

Explanation of Solution

Given:

X	y
2	2
4	1
8	$\frac{1}{2}$

Calculation:

The table is as follows.

X	2	4	8
Y	2	1	$\frac{1}{2}$

The objective is to determine whether the table or equation is an inverse or a direct variation.

In an inverse variation, the product of two values remains constant.

Direct variation gives $y=kx$ .

So,

  $\begin{array}{l}xy=k\\ 2\cdot 2=4\\ 4\cdot 1=4\\ 8\cdot \frac{1}{2}=4\end{array}$

Since the product of two values $xy$ are not constant. Hence, the table of variables is not an inverse variation.

Therefore, the table of values represents the inverse variation is $xy=4$ .

Conclusion:

The table of values represents the inverse variation is $xy=4$