1. What is Slope?

Slope measures the steepness and direction of a line. It represents the ratio of vertical change (rise) to horizontal change (run) between two points on a line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

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

Explanation: The numerator represents the vertical change (difference in y-values) while the denominator represents the horizontal change (difference in x-values).

3. Importance of Slope Calculation

Details: Slope is fundamental in algebra, geometry, calculus, physics, engineering, and many other fields. It describes rates of change in real-world situations like velocity, gradient, and trend analysis.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points on a line. The calculator will determine the slope. For vertical lines (where x₁ = x₂), the slope is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope mean?
A: A positive slope means the line rises as you move from left to right (increasing x-values).

Q2: What does a negative slope mean?
A: A negative slope means the line falls as you move from left to right (decreasing y-values as x increases).

Q3: What does zero slope mean?
A: A zero slope means the line is perfectly horizontal (no vertical change as x changes).

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

Q5: How is slope used in real life?
A: Slope concepts are used in road grading, roof pitch, wheelchair ramps, economics (supply/demand curves), and physics (velocity-time graphs).