1. What is Slope?

The slope of a line measures its steepness and direction. It's calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two distinct points on the 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 between the points, while the denominator represents the horizontal change.

3. Importance of Slope Calculation

Details: Slope is fundamental in algebra, calculus, physics, engineering, and many other fields. It describes rates of change, determines if lines are parallel or perpendicular, and appears in linear equations.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will determine the slope, or indicate if the slope is undefined (for vertical lines).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive/negative slope mean?
A: Positive slope means the line rises left-to-right. Negative slope means it falls left-to-right.

Q2: What does zero slope indicate?
A: A zero slope means the line is perfectly horizontal.

Q3: Why is slope undefined for vertical lines?
A: Because the denominator (x₂ - x₁) would be zero, and division by zero is undefined in mathematics.

Q4: How is slope related to angle?
A: The slope equals the tangent of the angle the line makes with the positive x-axis.

Q5: Can slope be used for non-linear functions?
A: For curves, slope at a point is given by the derivative at that point.