f(x2) - f(x1) average rate of change = X2 - X1 Calculate this average rate of change to show that it is the same as the slope m. f(x2) - f(x1) (mx2 + b) X2 - X1 X2 - X1 mx2 +b - b X2 - X1 %3D X2 - X1

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.9: Combining Functions
Problem 50HP
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If f(x) = mx + b is a linear function, then the average rate of change of f between any two real numbers x1 and xɔ is
f(x2) – F(x1)
%3D
average rate of change
X2 - X1
Calculate this average rate of change to show that it is the same as the slope m.
f(x2) – f(x1) _ (mx2 + b) – ( |
X2 - X1
X2 – X1
mx2
+ b – b
X2 - X1
m
%|
X2 - X1
showing that the average rate of change --Select--- v the same as the slope m.
Transcribed Image Text:If f(x) = mx + b is a linear function, then the average rate of change of f between any two real numbers x1 and xɔ is f(x2) – F(x1) %3D average rate of change X2 - X1 Calculate this average rate of change to show that it is the same as the slope m. f(x2) – f(x1) _ (mx2 + b) – ( | X2 - X1 X2 – X1 mx2 + b – b X2 - X1 m %| X2 - X1 showing that the average rate of change --Select--- v the same as the slope m.
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