1. What is Rate of Change?

The rate of change (ROC) measures how much one quantity changes in relation to another quantity. It represents the ratio of the vertical change between two points to the horizontal change between those same two points.

2. How Does the Calculator Work?

The calculator uses the rate of change formula:

Where:

• \( y2 \) — Second y-coordinate value
• \( y1 \) — First y-coordinate value
• \( x2 \) — Second x-coordinate value
• \( x1 \) — First x-coordinate value

Explanation: The formula calculates the change in the y-values divided by the change in the x-values between two points.

3. Importance of Rate of Change

Details: Rate of change is fundamental in mathematics, physics, economics, and many other fields. It represents slope in geometry, velocity in physics, and marginal changes in economics.

4. Using the Calculator

Tips: Enter the coordinates of two points (x1,y1) and (x2,y2). The calculator will compute the rate of change between them. Ensure x2 ≠ x1 to avoid division by zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive rate of change indicate?
A: A positive ROC indicates an increasing relationship - as x increases, y increases.

Q2: What does a negative rate of change mean?
A: A negative ROC indicates a decreasing relationship - as x increases, y decreases.

Q3: What does a zero rate of change mean?
A: A zero ROC (when y2 = y1) indicates no change - y remains constant as x changes.

Q4: What if the denominator (x2 - x1) is zero?
A: The rate of change is undefined as it would require division by zero. This represents a vertical line.

Q5: How is rate of change different from percentage change?
A: Rate of change measures absolute change per unit, while percentage change measures relative change compared to the original value.