1. What is Slope?

The slope of a line measures its steepness and direction. It represents the ratio of vertical change (rise) to horizontal change (run) 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 the first point
• \( (x_2, y_2) \) — Coordinates of the second point

Explanation: The numerator represents the vertical change between points, while the denominator represents the horizontal change.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It describes rates of change, helps determine if lines are parallel or perpendicular, and is essential in calculus concepts like derivatives.

4. Using the Calculator

Tips: Enter coordinates for two distinct points on the line. If x-coordinates are equal, the line is vertical with undefined slope. If y-coordinates are equal, the line is horizontal with zero slope.

5. Frequently Asked Questions (FAQ)

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

Q2: What's the slope of a horizontal line?
A: Zero, since there's no vertical change (y₂ - y₁ = 0).

Q3: What's the slope of a vertical line?
A: Undefined, since there's no horizontal change (x₂ - x₁ = 0) leading to division by zero.

Q4: How is slope related to angle?
A: The angle θ a line makes with the positive x-axis relates to slope by tan(θ) = slope.

Q5: Can slope be used for nonlinear functions?
A: For curves, slope varies at each point and is given by the derivative at that point.