What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

The rate of change is the slope. m = slope. We can see that the rate of change is going to be -2 because the function f(x) = −2x + 1 is in the slope intercept form and is linear, which slope intercept form is y = mx + b. Remember m = slope = rate of change.

There are a few methods to finding the average rate of change. A popular one is using the slope formula:

Slope Formula
m = slope = rate of change



Now we know the formula for rate of change, we can use this but first to use this formula we need some points. We get our points by plugging in -5 and 1 into our equation f(x) = -2x + 1

f(x) = -2x + 1
f(x) = -2(-5) + 1
f(x) = 10 + 1
f(x) = 11
So y = 11 when x = -5. We have our first point, which is (-5, 11)

Lets find our next point
f(x) = -2x + 1
f(x) = -2(1)+ 1
f(x) = -2+ 1
f(x) = -1

So y = -1 when x = 1. We have our second point, which is (1, -1)

Now we can find the rate of change by using our slope formula and our two points: (-5, 11) and (1,-1)






rate of change = -2