Question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 ≤ x ≤ 15.

Answer 1

The average rate of change is also known as "Slope".

The formula for calculate the slope is the following:

`m=(y_2-y_1)/(x_2-x_1)`

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:

`10\le x\le15`

You need to find the corresponding y-values for:

`\begin{gathered} x_1=10 \\ x_2=15 \end{gathered}`

As you can identify in the table, when the value of "x" is:

`x=10`

The value of "y" is:

`y=30`

And when

`x=15`

The value of "y" is:

`y=24`

Therefore, you can set up that:

`\begin{gathered} y_2=24 \\ y_1=30 \\ x_2=15 \\ x_1=10 \end{gathered}`

Now you can substitute values into the formula and evaluate:

`m=(24-30)/(15-10)=-(6)/(5)=-1.2`

The answers is:

`-1.2`