1. What is the Slope Formula?

The slope formula calculates the steepness or incline of a line between two points in a coordinate system. It represents the rate of change between the y-coordinates and x-coordinates of two distinct points.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

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

Explanation: The formula calculates the ratio of vertical change (rise) to horizontal change (run) between two points on a line.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It helps determine the direction and steepness of lines, rates of change, and is essential in calculus and linear algebra.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The x-coordinates must be different (x₁ ≠ x₂) to avoid division by zero. The calculator will compute the slope or indicate if it's undefined (vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line rises from left to right, showing a positive relationship between variables.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line falls from left to right, showing an inverse relationship between variables.

Q3: When is slope undefined?
A: Slope is undefined when x₁ = x₂, which represents a vertical line where there is no horizontal change.

Q4: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line where there is no vertical change between points.

Q5: Can slope be used for non-linear functions?
A: The slope formula calculates the average slope between two points. For non-linear functions, the slope at a specific point is calculated using derivatives.