1. What is Rate of Change?

The Rate of Change (ROC) measures how much one quantity changes in relation to another quantity. In graphs, it represents the slope of the line between two points (x₁,y₁) and (x₂,y₂).

2. How Does the Calculator Work?

The calculator uses the Rate of Change formula:

Where:

• \( y2 \) — Y-coordinate of second point
• \( y1 \) — Y-coordinate of first point
• \( x2 \) — X-coordinate of second point
• \( x1 \) — X-coordinate of first point

Explanation: The formula calculates the ratio of vertical change (Δy) to horizontal change (Δx) between two points on a graph.

3. Importance of Rate of Change

Details: Rate of Change is fundamental in mathematics, physics, economics, and engineering. It describes speed, velocity, growth rates, and other dynamic relationships between variables.

4. Using the Calculator

Tips: Enter the coordinates of two points on a graph. The calculator will determine the slope or 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-values are increasing as x-values increase (upward slope).

Q2: What does a negative ROC indicate?
A: A negative ROC means the y-values are decreasing as x-values increase (downward slope).

Q3: What does ROC = 0 mean?
A: A zero ROC indicates no change in y-values as x-values change (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 used in real-world applications?
A: ROC is used to calculate speed (distance vs time), growth rates (population vs time), and economic indicators (price vs time).