Chapter 11, Problem 1STP

To determine

To find: whether the table or equation is an inverse or a direct variation.

Answer to Problem 1STP

The table of values represents the inverse variation is $xy=-128$ . And the correct option is D

Explanation of Solution

Given:

X	y
-8	16
-4	32
2	-64
8	-16
16	-8

Calculation:

The table is as follows.

X	-8	-4	2	8	16
Y	16	32	-64	-16	-8

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,

  $\begin{array}{l}xy=k\\ -8\cdot 16=-128\\ -4\cdot 32=-128\\ 2\cdot \left(-64\right)=-128\end{array}$

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

Hence, the table of values represents the inverse variation is $xy=-128$ . And the correct option is D

Conclusion:

The table of values represents the inverse variation is $xy=-128$ . And the correct option is D