Chapter 9.7, Problem 16PPS

To determine

Whether the given data represents linear or non-linear function

Answer to Problem 16PPS

It is a 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,

  $\begin{array}{l}{m}_1=\frac{16-21}{2-1}\\ m_1=\frac{-5}{1}=-5\\ \\ m_2=\frac{11-16}{3-2}\\ m_2=\frac{-5}{1}=-5\\ \\ m_3=\frac{6-11}{4-3}\\ m_3=\frac{-5}{1}=-5\end{array}$

As m1=m2=m3, the slope is constant, hence, the given data represents a linear function.