1. What is Slope?

Slope is a measure of the steepness or incline 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 (unitless)
• \( y_2, y_1 \) — Y-coordinates of two points
• \( x_2, x_1 \) — X-coordinates of two points

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

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It helps determine rates of change, gradients, and linear relationships between variables.

4. Using the Calculator

Tips: Enter coordinates for two distinct points. The calculator will compute the slope. If points have the same x-coordinate, 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 does zero slope mean?
A: Zero slope indicates a horizontal line where y-values remain constant regardless of x-values.

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

Q5: Can slope be used for non-linear functions?
A: For non-linear functions, slope represents the instantaneous rate of change at a specific point (derivative).