an = 9 + (n−1)(2)
The rate of change of this linear function is the rate of change of this arithmetic sequence.
The rate of change of a linear function is equal to the common difference of the arithmetic sequence.
In this case, the linear function is an = 9 + (n−1)(2). To find the rate of change, we can first simplify the equation:
an = 9 + 2n − 2
Next, we can rearrange the equation to isolate the term with n on one side:
an - 9 = 2n - 2
Now, we can combine like terms:
an - 2n = 9 - 2
Simplifying further:
-an = 7
Finally, we can divide both sides of the equation by -1 to solve for n:
n = -7
Therefore, the rate of change of this linear function is -7, which means that the common difference of the arithmetic sequence is -7.