1. What is Slope?

Slope is a measure of the steepness of a line, representing the rate of change between two variables. It describes how much the y-value changes for each unit change in the x-value.

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 slope represents the ratio of vertical change (rise) to horizontal change (run) between two points on a line.

3. Importance of Slope Calculation

Details: Slope calculation is fundamental in mathematics, physics, engineering, and economics. It helps determine rates of change, linear relationships, and is essential for understanding linear equations and graphing.

4. Using the Calculator

Tips: Enter the coordinates of two points (x₁,y₁) and (x₂,y₂). The calculator will compute the slope. If x₂ = x₁, the slope is undefined (vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that as x increases, y also increases - the line rises from left to right.

Q2: What does a negative slope indicate?
A: A negative slope indicates that as x increases, y decreases - the line falls from left to right.

Q3: What is a zero slope?
A: A zero slope indicates a horizontal line where y remains constant regardless of x changes.

Q4: When is slope undefined?
A: Slope is undefined when x₂ = x₁, indicating a vertical line where the run is zero.

Q5: Can slope be used for non-linear functions?
A: The slope formula applies only to linear functions. For non-linear functions, we use derivatives to find instantaneous slope at specific points.