1. What is Rate of Change?

The Rate of Change (ROC) measures how much one quantity changes relative to another. In mathematics, it represents the slope of the line connecting two points on a graph (y2-y1)/(x2-x1).

2. How Does the Calculator Work?

The calculator uses the Rate of Change formula:

Where:

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

Explanation: The formula calculates the slope between two points, representing how much the y-value changes per unit change in the x-value.

3. Importance of Rate of Change

Details: Rate of change is fundamental in calculus, physics, economics, and other sciences. It describes velocity, growth rates, marginal costs, and other dynamic phenomena.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does a positive/negative ROC indicate?
A: Positive ROC means increasing values (rising line), negative means decreasing values (falling line).

Q2: What if x2 equals x1?
A: This creates a vertical line with undefined slope (infinite ROC), which the calculator cannot compute.

Q3: How is ROC different from percentage change?
A: ROC measures absolute change per unit, while percentage change measures relative change compared to initial value.

Q4: Can ROC be used for non-linear functions?
A: This calculates average ROC between two points. For instantaneous ROC at a point, calculus (derivative) is needed.

Q5: What are common applications of ROC?
A: Used in physics (velocity), economics (marginal analysis), biology (growth rates), and engineering (signal processing).