Chapter 3.5, Problem 57E

To determine

To determine whether the below equation represents a linear or non-linear function:

  $y-9=\frac{2}{x}$

Answer to Problem 57E

Non-linear function.

Explanation of Solution

Given:

  $y-9=\frac{2}{x}$

Concept Used:

A linear function is written in the form

  $y=ax+b$

Calculation:

In order to identify whether the equation

  $y-9=\frac{2}{x}$

represents a linear or non-linear function. Check whether the given equation can be written in the form of a standard linear function $y=ax+b$ .

First simplify the equation so that variable is on one side of the equation and rest is another, as

  $\begin{array}{c}y-9=\frac{2}{x}\\ \Rightarrow y=\frac{2}{x}+9\end{array}$

Since,

  $\begin{array}{c}y=\frac{2}{x}+9\\ \ne ax+b\end{array}$

As, in given equation degree of variable x is not 1, so it can’t be written in the form $y=ax+b$ .

Thus, given equation is not a linear function.

Thus, given equation is a non-linear function.