Chapter 8.1, Problem 12PPSE

Solution

To find the function and graph the function and find $y$ when $x=10$ for given set of values.

  $y=\frac{1}{10}\text{when }x=10$ .

  

Given information:

The variables are:

  $x=1,y=1$

Also given that the set of given variables are in inverse variation.

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)

Calculation:

From above, the function is,

Put $x=1,y=1$

  $\begin{array}{l}k=\left(1\right)\left(1\right)\\ k=1\end{array}$

Now, it is given that $x=10$ , hence the function is,

  $\begin{array}{l}1=xy\\ y=\frac{1}{x}\end{array}$

Now put $x=10$

  $\begin{array}{l}1=\left(10\right)\left(y\right)\\ y=\frac{1}{10}\end{array}$

Now to Graph of the function $y=\frac{1}{x}$ , find the points on graph and then join.

$x$	1	2	4	5
$y$	1	0.5	0.25	0.2

  

Conclusion:

Hence, the function is $y=\frac{1}{x}$