Chapter 9.7, Problem 17PPS

To determine

Whether the given data represents linear or non-linear function

Answer to Problem 17PPS

It is a non-linear function

Explanation of Solution

Given:

The given data is

  

Calculation:

Linear Functions: The graph of linear functions is always a straight line. These functions have the form $y=a+bx$ .

The slope of the linear graph always remains constant. The slope of the equation is given by:

  $m=\frac{y_2-y_1}{x_2-x_1}$

From the given table,

  $\begin{array}{l}{m}_1=\frac{8-5}{0-\left(-2\right)}\\ m_1=\frac{3}{2}\\ \\ m_2=\frac{10-8}{2-0}\\ m_2=\frac{2}{2}=1\\ \\ m_3=\frac{15-10}{4-2}\\ m_3=\frac{5}{2}\end{array}$

As m1 is not equal to m2 is not equal to m3, the slope is not constant, hence, the given data represents a non-linear function.