1. What is the Gradient of a Line?

The gradient (or slope) of a line measures its steepness and direction. It represents the rate of change between two points on a line and is fundamental in mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( m \) — Slope or gradient (dimensionless)
• \( x_1, y_1 \) — Coordinates of the first point
• \( x_2, y_2 \) — Coordinates of the second point

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

3. Importance of Slope Calculation

Details: Slope calculation is essential in algebra, geometry, calculus, physics (velocity, acceleration), engineering (gradients, inclines), and data analysis (trend lines).

4. Using the Calculator

Tips: Enter coordinates for two distinct points. The calculator will compute the slope. If x₂ = x₁, the line is vertical and the slope is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates the line rises from left to right, showing a positive relationship between variables.

Q2: What does a negative slope indicate?
A: A negative slope indicates the line falls from left to right, showing an inverse relationship between variables.

Q3: What is a zero slope?
A: A zero slope indicates a horizontal line where y-values remain constant regardless of x-values.

Q4: Why is slope undefined for vertical lines?
A: Vertical lines have undefined slope because division by zero occurs in the formula (x₂ - x₁ = 0).

Q5: How is slope used in real-world applications?
A: Slope is used in road gradients, roof pitches, economic graphs, physics motion analysis, and engineering design calculations.