Rate of Change

Enter Your Data

Two Points

Function Table

Point 1 (x₁, y₁)

x₁

y₁

Point 2 (x₂, y₂)

x₂

y₂

Try an example:

x	y

Try an example:

Result

Enter two points or fill the table, then press Calculate Rate of Change to see the answer and every step.

Average Rate of Change

Δy / Δx — — = —

📐

This is the slope m of the line through these two points. Rate of change and slope are the same concept: how steeply y changes per unit of x.

Rates Between Consecutive Rows

From x	To x	Δy	Δx	Rate

Rate of Change = Slope

Rate = Δy / Δx = (y₂ − y₁) / (x₂ − x₁)

The average rate of change measures how much the output (y) changes for every one-unit increase in the input (x) between two points.

It is identical to the slope formula — both describe the steepness of a line connecting two points.

Real-world examples:

A positive rate means y increases as x increases; a negative rate means y decreases.

Linear vs Non-Linear Functions

Constant rate → Linear | Variable rate → Non-linear

A function is linear when the rate of change is the same between every pair of consecutive points in a table.

When the rate changes from interval to interval, the function is non-linear (quadratic, exponential, etc.).

Check linearity fast: subtract consecutive y-values. If the differences are equal, the function is linear.