Final answer:
The average rate of change of a linear function can be found by calculating the difference in function values between two points and dividing it by the difference in the x-values. For the given function, g(x) = -9x + 4, the average rate of change between x = a and x = b is (-9b + 9a)/(b - a).
Step-by-step explanation:
The average rate of change of a linear function between two points can be found by calculating the difference in function values between the two points and dividing it by the difference in the x-values of the points. In this case, the linear function is g(x) = -9x + 4. To find the average rate of change between x = a and x = b, we substitute these values into the function, calculate the difference in function values, and divide it by the difference in the x-values.
Let's say x = a and x = b, substituting these values into the function gives us g(a) = -9a + 4 and g(b) = -9b + 4. The average rate of change is then given by (g(b) - g(a))/(b - a), which simplifies to (-9b + 4 - (-9a + 4))/(b - a) = (-9b + 9a)/(b - a).
For example, if a = 2 and b = 5, the average rate of change is (-9(5) + 9(2))/(5 - 2) = (-45 + 18)/3 = -9.