Question

Calculate the average rate of change between consecutive data points in parts to determine whether the output in each table is a linear function of the input. input: 2 7 9 14 output: 0 15 18 20 Select the correct choice below and if necessary, fill in the answer box to complete your choice. a) The average rate of change between consecutive data points in table b is ___. The out is a linear function of the input. b) The output is not a linear function of the input

Answer 1

Given:

Find-: Rate of change or check linear function.

Sol:

Rate of change is:

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

Where,

$\begin{gathered} (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}$

So the rate of change.

$\begin{gathered} =\frac{15-0}{7-2} \\ \\ =\frac{15}{5} \\ \\ =3 \end{gathered}$

The second point is:

$\begin{gathered} =\frac{18-15}{9-7} \\ \\ =\frac{3}{2} \end{gathered}$

So rate change is different from the other point so it is not a linear function.