1. What is Slope?

Slope is a measure of the steepness of a line, representing the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. It describes both the direction and the steepness of the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( m \) — Slope of the line (unitless)
• \( x_1 \) — x-coordinate of the first point
• \( y_1 \) — y-coordinate of the first point
• \( x_2 \) — x-coordinate of the second point
• \( y_2 \) — y-coordinate of the second point

Explanation: The formula calculates the ratio of vertical change to horizontal change between two distinct points on a line.

3. Importance of Slope Calculation

Details: Slope is a fundamental concept in mathematics, physics, engineering, and economics. It's used to describe rates of change, linear relationships, and is essential in calculus for finding derivatives.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will compute the slope. If the x-coordinates are equal (x₂ = x₁), the slope is undefined as it represents a vertical line.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line rises as it moves from left to right.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line falls as it moves from left to right.

Q3: What does a zero slope mean?
A: A zero slope indicates a horizontal line, where y-values remain constant.

Q4: When is slope undefined?
A: Slope is undefined when x₂ = x₁, which represents a vertical line.

Q5: Can slope be used for non-linear functions?
A: The slope formula calculates the average rate of change between two points, but for non-linear functions, the slope varies at different points along the curve.