1. What is Gradient of a Graph?

The gradient (or slope) of a graph measures how steep a line is. It represents the rate of change of y with respect to x. A positive gradient means the line is increasing, negative means decreasing, and zero means horizontal.

2. How Does the Calculator Work?

The calculator uses the gradient formula:

Where:

• \( (x_1, y_1) \) — First point coordinates
• \( (x_2, y_2) \) — Second point coordinates
• \( m \) — Gradient (slope) of the line

Explanation: The formula calculates the ratio of vertical change to horizontal change between two points on a line.

3. Importance of Gradient Calculation

Details: Gradient is fundamental in mathematics and physics. It's used in calculating rates of change, determining direction of lines, analyzing motion, and in calculus as the derivative at a point.

4. Using the Calculator

Tips: Enter coordinates for two distinct points on a line. The calculator will determine the gradient. For vertical lines (where x-coordinates are equal), the gradient is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a gradient of 2 mean?
A: A gradient of 2 means for every 1 unit increase in x, y increases by 2 units.

Q2: What's the gradient of a horizontal line?
A: The gradient is 0 because there's no vertical change (y₂ - y₁ = 0).

Q3: Can gradient be negative?
A: Yes, a negative gradient means the line is decreasing (as x increases, y decreases).

Q4: Why is gradient undefined for vertical lines?
A: Because x₂ - x₁ = 0, and division by zero is undefined in mathematics.

Q5: How is gradient related to real-world applications?
A: Gradient represents rates like speed (distance vs time), cost rates, or any change measurement in science and economics.