1. What is Gradient of a Line?

The gradient (or slope) of a line measures its steepness and direction. It's a fundamental concept in coordinate geometry that describes how much a line rises or falls as it moves horizontally.

2. How Does the Calculator Work?

The calculator uses the gradient formula:

Where:

• \( m \) — Gradient (slope) of the line
• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point

Explanation: The gradient represents the ratio of vertical change (rise) to horizontal change (run) between two points on a line.

3. Importance of Gradient Calculation

Details: Gradient is essential in mathematics, physics, engineering, and many other fields. It helps determine the rate of change, direction of lines, and is fundamental in calculus concepts like derivatives.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points on a line. The calculator will compute the gradient. If the points have the same x-coordinate, the line is vertical and the gradient is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive gradient mean?
A: A positive gradient means the line rises as it moves from left to right.

Q2: What does a negative gradient mean?
A: A negative gradient means the line falls as it moves from left to right.

Q3: What does a zero gradient mean?
A: A zero gradient means the line is perfectly horizontal.

Q4: Why is gradient undefined for vertical lines?
A: Because the run (x₂ - x₁) is zero, and division by zero is undefined in mathematics.

Q5: How is gradient related to angle?
A: The gradient equals the tangent of the angle the line makes with the positive x-axis.