The average rate of change is also known as "Slope".
The formula for calculate the slope is the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
As you can notice, it can be found dividing the change in "y" by the change in "x".
In this case you have the table of a function and you need to find the rate of change over this interval:
[tex]10\le x\le15[/tex]
You need to find the corresponding y-values for:
[tex]\begin{gathered} x_1=10 \\ x_2=15 \end{gathered}[/tex]
As you can identify in the table, when the value of "x" is:
[tex]x=10[/tex]
The value of "y" is:
[tex]y=30[/tex]
And when
[tex]x=15[/tex]
The value of "y" is:
[tex]y=24[/tex]
Therefore, you can set up that:
[tex]\begin{gathered} y_2=24 \\ y_1=30 \\ x_2=15 \\ x_1=10 \end{gathered}[/tex]
Now you can substitute values into the formula and evaluate:
[tex]m=\frac{24-30}{15-10}=-\frac{6}{5}=-1.2[/tex]
The answers is:
[tex]-1.2[/tex]
