Chapter 8.1, Problem 1LC

Solution

To find: The relationship between the variables in given case is direct variation, an inverse variation, or nether.

Given variables are in inverse variation.

Given information:

The table is:

$x$	$y$
1	2
3	6
12	0.5
15	0.4

Concept:

Inverse variation: When one of the given variables increases with decrease in other variable, then it is inverse variation or vice versa.

It can be represented as:

  $xy=k$ (Product of variables remains constant)

Direct variation: When one variable increases with increase in other variable, or decreases with decrease in other variable then it is direct variation.

Calculation:

From the given table:

  $\begin{array}{l}1\times 6=6\\ 3\times 2=6\\ 12\times 0.5=6\\ 15\times 0.4=6\end{array}$

As product is constant, it is inverse variation.

Conclusion:

Hence, given variables are in inverse variation.