Final answer:
The rate of change of a function graphed as a straight line through points (3, −27) and (−1, 9) is calculated using the slope formula and is −9.
Step-by-step explanation:
The rate of change of a function represented by a straight line can be determined by calculating the slope of that line. To find the slope between two points on a line, you can use the formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of the two points the line passes through.
In this case, we have the points (3, −27) and (−1, 9). Applying the slope formula, we get:
slope = (9 - (−27)) / ((−1) - 3)
slope = 36 / (−4)
slope = −9
So the rate of change of the line is −9, meaning for every increase of 1 unit on the x-axis, there is a decrease of 9 units on the y-axis. This slope is consistent along the entire length of a straight line.