Average Rate of Change from a Graph Calculator

Average Rate of Change Calculator

Understanding the Average Rate of Change

The average rate of change of a function between two points on its graph represents the slope of the secant line connecting those two points. It tells us how much the function's output (y-value) changes, on average, for each unit change in the input (x-value) over a given interval.

Formula:

The formula for the average rate of change of a function $f(x)$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$$ \text{Average Rate of Change} = \frac{y_2 – y_1}{x_2 – x_1} $$

This is identical to the slope formula ($m$) in coordinate geometry, often remembered as "rise over run".

How to Use This Calculator:

1. Identify the coordinates of two points on the graph of your function. These will be in the form $(x, y)$.
2. Enter the x-coordinate of the first point into the "X1 Coordinate" field.
3. Enter the y-coordinate of the first point into the "Y1 Coordinate" field.
4. Enter the x-coordinate of the second point into the "X2 Coordinate" field.
5. Enter the y-coordinate of the second point into the "Y2 Coordinate" field.
6. Click the "Calculate" button.

The calculator will then display the average rate of change between these two points.

Example:

Suppose you have a graph of a function and you want to find the average rate of change between the point (2, 5) and the point (7, 15).

• X1 Coordinate: 2
• Y1 Coordinate: 5
• X2 Coordinate: 7
• Y2 Coordinate: 15

Using the formula:

$$ \text{Average Rate of Change} = \frac{15 – 5}{7 – 2} = \frac{10}{5} = 2 $$

The average rate of change between these two points is 2. This means that for every unit increase in x, the function's output y increases by an average of 2 units over this interval.