Chapter 3.5, Problem 58E

To determine

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

$x=2+15y$

Answer to Problem 58E

Linear function.

Explanation of Solution

Given:

$x=2+15y$

Concept Used:

A linear function is written in the form

$y=ax+b$

Calculation:

In order to identify whether the equation

$x=2+15y$

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

$\begin{array}{c}x=2+15y\\ \Rightarrow 2+15y=x\\ \Rightarrow 15y=x-2\\ \Rightarrow y=\frac{x-2}{15}\end{array}$

Now,

  $\begin{array}{c}y=\frac{x-2}{15}\\ =\frac{1}{15}x-\frac{2}{15}\\ =ax+b;\text{ where }a=\frac{1}{15},b=-\frac{2}{15}\end{array}$

Thus, the given equation can be rewritten in the form $y=ax+b$ .

Thus, given equation is a linear function.