1. What is Rate of Change?

The Rate of Change (ROC) measures how much one quantity changes relative to another quantity. In mathematics, it represents the ratio of the vertical change (Δy) to the horizontal change (Δx) between two points on a line.

2. How Does the Calculator Work?

The calculator uses the Rate of Change formula:

Where:

• \( y_2 \) — Second y-coordinate
• \( y_1 \) — First y-coordinate
• \( x_2 \) — Second x-coordinate
• \( x_1 \) — First x-coordinate

Explanation: The formula calculates the slope of the straight line connecting two points (x₁,y₁) and (x₂,y₂) in the Cartesian coordinate system.

3. Importance of Rate of Change

Details: Rate of Change is fundamental in calculus, physics, economics, and many other fields. It describes how quickly or slowly something changes over time or space.

4. Using the Calculator

Tips: Enter the coordinates of two points. 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 ROC indicate?
A: A positive ROC means the y-value increases as the x-value increases (positive slope).

Q2: What does a negative ROC indicate?
A: A negative ROC means the y-value decreases as the x-value increases (negative slope).

Q3: What does ROC = 0 mean?
A: A zero ROC indicates no change in y as x changes (horizontal line).

Q4: What if the denominator (x₂ - x₁) is zero?
A: This results in an undefined ROC, representing a vertical line (infinite slope).

Q5: How is ROC different from percentage change?
A: ROC gives the absolute change per unit, while percentage change expresses the relative change compared to the original value.