Solution:
Given:
The table:
The rate of change is gotten by using the slope formula;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ where: \\ x\text{ is the input} \\ y\text{ is the output} \end{gathered}[/tex]To get the rate of change between inputs -5 and 0
[tex]\begin{gathered} The\text{ points are:} \\ (-5,-50)\text{ and }(0,-5) \\ where: \\ x_1=-5,y_1=-50 \\ x_2=0,y_2=-5 \\ \\ Hence, \\ m=\frac{-5-(-50)}{0-(-5)} \\ m=\frac{-5+50}{0+5} \\ m=\frac{45}{5} \\ m=9 \end{gathered}[/tex]To get the rate of change between inputs 0 and 5
[tex]\begin{gathered} The\text{ points are:} \\ (0,-5)\text{ and }(5,40) \\ where: \\ x_1=0,y_1=-5 \\ x_2=5,y_2=40 \\ \\ Hence, \\ m=\frac{40-(-5)}{5-0} \\ m=\frac{40+5}{5-0} \\ m=\frac{45}{5} \\ m=9 \end{gathered}[/tex]To get the rate of change between inputs 5 and 8
[tex]\begin{gathered} The\text{ points are:} \\ (5,40)\text{ and }(8,67) \\ where: \\ x_1=5,y_1=40 \\ x_2=8,y_2=67 \\ \\ Hence, \\ m=\frac{67-40}{8-5} \\ m=\frac{27}{3} \\ m=9 \end{gathered}[/tex]From the calculations, it can be seen that the rate of change for each consecutive point is 9.
Therefore, the average rate of change between consecutive data points in table A is 9.
Thus, the output is a linear function of the input.
