Average Rate of Change Calculator
Use this tool to calculate the average rate of change between two points on a function. This represents the slope of the secant line passing through (x₁, y₁) and (x₂, y₂).
Calculation Result
Understanding the Average Rate of Change
The average rate of change measures how much a function's output (y) changes relative to the change in its input (x) over a specific interval. In geometry, this is equivalent to the slope of the secant line connecting two points on a graph. In physics, if the function represents position over time, the average rate of change is the average velocity.
The Formula
A = [f(x₂) – f(x₁)] / (x₂ – x₁)
How to Use This Calculator
- Step 1: Identify your first point coordinates (x₁, y₁).
- Step 2: Identify your second point coordinates (x₂, y₂).
- Step 3: Enter the values into the respective fields above.
- Step 4: Click "Calculate" to find the slope between those two points.
Example Calculation
Suppose a car travels from point A (time = 1 hour, distance = 50 miles) to point B (time = 3 hours, distance = 160 miles). To find the average speed (rate of change):
- x₁ = 1, y₁ = 50
- x₂ = 3, y₂ = 160
- Calculation: (160 – 50) / (3 – 1) = 110 / 2 = 55 miles per hour