1. What is Slope?

Slope measures the steepness and direction of a line, calculated as the ratio of vertical change (Δy) to horizontal change (Δx) between two points on the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( (x_1, y_1) \) — Coordinates of first point
• \( (x_2, y_2) \) — Coordinates of second point
• \( \Delta y \) — Change in y-direction (y₂ - y₁)
• \( \Delta x \) — Change in x-direction (x₂ - x₁)

Explanation: The slope represents how much y changes for each unit change in x. Positive slope means the line rises, negative means it falls, zero means horizontal, and undefined means vertical.

3. Importance of Slope Calculation

Details: Slope is fundamental in algebra, geometry, calculus, physics, engineering, and economics. It describes rates of change in real-world phenomena like velocity, cost functions, and gradients.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 0 mean?
A: A slope of 0 indicates a horizontal line (no vertical change as x changes).

Q2: Why is slope undefined for vertical lines?
A: Because Δx = 0, making division by zero undefined in mathematics.

Q3: How is slope related to angle?
A: The angle θ of inclination relates to slope m by: \( m = \tan(\theta) \).

Q4: Can slope be a fraction?
A: Yes, slope can be any real number - integer, fraction, or decimal.

Q5: What's the difference between positive and negative slope?
A: Positive slope rises left-to-right; negative slope falls left-to-right.