Chapter 3.2, Problem 24E

To determine

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

$2x+3y=9xy$

Answer to Problem 24E

Non-linear function.

Explanation of Solution

Given:

$2x+3y=9xy$

Concept Used:

A linear function is written in the form

$y=ax+b$

Calculation:

In order to identify whether the equation

$2x+3y=9xy$

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, as

$\begin{array}{c}2x+3y=9xy\\ \Rightarrow 3y=9xy-2x\\ \Rightarrow 3y-9xy=2x\\ \Rightarrow \left(3-9x\right)y=2x\\ \Rightarrow y=\frac{2x}{3-9x}\end{array}$

Since,

$\begin{array}{c}y=\frac{2x}{3-9x}\\ \ne ax+b\end{array}$

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.