Rate of Change and Initial Value

In a linear function f(x) = mx + b: - Rate of change = m = slope = how fast the output changes per unit of input - Initial value = b = y-intercept = the output when the input is 0 The rate of change is constant for linear functions — that's what makes them linear! No matter which two points you pick, frac{Delta y}{Delta x} is always the same.

The average rate of change of a function f from x = a to x = b is: [formula] For linear functions, this equals the slope everywhere. For nonlinear functions, it varies depending on the interval (we'll cover this later).

Example: A plant is 3 cm tall at week 0 and 15 cm tall at week 4. What is the average growth rate?