Chapter 8.4, Problem 1GP

To determine

To calculate: To find the rate of change of linear function

Answer to Problem 1GP

The rate of change of linear function is $\frac{1}{2}$

Explanation of Solution

Given information: Linear function is

  

Formula Used:

Rate of change is constant for a linear function and is calculated vertical change between two points, called as rise and the horizontal change between the two points, called as run.

  $Rateofchange=\frac{Rise}{Run}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Linear function is given as follows:

  

Let two points on graph be $\left(10,5\right)$ and $\left(20,10\right)$

Rate of change is calculated as

  $Rateofchange=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values in above,

  $\begin{array}{l}Rateofchange=\frac{10-5}{20-10}\\ Rateofchange=\frac{5}{10}\\ Rateofchange=\frac{1}{2}\end{array}$

Hence, rate of change is $\frac{1}{2}$