Average Rate of Change Equation Calculator

Average Rate of Change Calculator

Understanding the Average Rate of Change

The average rate of change of a function measures how much the function's output (y-value) changes, on average, for a given change in its input (x-value) over a specific interval. It essentially tells you the slope of the secant line connecting two points on the graph of the function.

The 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 given by:

Average Rate of Change = \(\frac{\Delta y}{\Delta x} = \frac{y_2 – y_1}{x_2 – x_1}\)

Where:

• \(\Delta y\) represents the change in the y-values.
• \(\Delta x\) represents the change in the x-values.
• \((x_1, y_1)\) are the coordinates of the first point.
• \((x_2, y_2)\) are the coordinates of the second point.

How to Use the Calculator

To find the average rate of change using this calculator, simply input the coordinates of two points that lie on the function you are analyzing.

1. Enter the first x-value (\(x_1\)) in the corresponding field.
2. Enter the first y-value (\(y_1\)) in the corresponding field.
3. Enter the second x-value (\(x_2\)) in the corresponding field.
4. Enter the second y-value (\(y_2\)) in the corresponding field.
5. Click the "Calculate Average Rate of Change" button.

The calculator will then display the average rate of change for the interval defined by these two points.

Example Calculation

Let's consider a function passing through the points \((2, 5)\) and \((7, 15)\).

• \(x_1 = 2\)
• \(y_1 = 5\)
• \(x_2 = 7\)
• \(y_2 = 15\)

Using the formula:

Average Rate of Change = \(\frac{15 – 5}{7 – 2} = \frac{10}{5} = 2\)

Therefore, the average rate of change of the function between \(x=2\) and \(x=7\) is 2. This means that, on average, for every 1-unit increase in x, the y-value increases by 2 units over this interval.

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