Chapter 5.1, Problem 22E

Solution

To determine: The variables $x\text{ and }y$ show direct variation, inverse variation or neither.

The variables $x\text{ and }y$ show neither variation.

Given information:

The values are:

$x$	$y$
$\begin{array}{l}4\\ 5\\ 6.2\\ 7\\ 11\end{array}$	$\begin{array}{l}16\\ 11\\ 10\\ 9\\ 6\end{array}$

Formula used:

Two variables $x\text{ and }y$ show direct variation if they are related as below:

  $y=ax$.

Two variables $x\text{ and }y$ show inverse variation if they are related as below:

  $y=\frac{a}{x}$.

Where, $a$ is a constant.

Explanation:

Consider the table and find the value of $x\cdot y$.

$x$	$y$	$x\cdot y$
$\begin{array}{l}4\\ 5\\ 6.2\\ 7\\ 11\end{array}$	$\begin{array}{l}16\\ 11\\ 10\\ 9\\ 6\end{array}$	$\begin{array}{l}64\\ 55\\ 62\\ 63\\ 66\end{array}$

The value $x\cdot y$ is not equal for each pair of data, so find $\frac{y}{x}$.

$x$	$y$	$\frac{y}{x}$
$\begin{array}{l}4\\ 5\\ 6.2\\ 7\\ 11\end{array}$	$\begin{array}{l}16\\ 11\\ 10\\ 9\\ 6\end{array}$	$\begin{array}{l}4\\ 2.2\\ 1.61\\ 1.3\\ 0.55\end{array}$

The value $\frac{y}{x}$ is also not equal for each pair of data.

Therefore, $x\text{ and }y$ show neither variation.