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 the vertical change between two points to the horizontal change between the same two points.

3. Importance of Slope Calculation

Details: Slope is a fundamental concept in mathematics, physics, engineering, and many other fields. It's used to describe rates of change, gradients, and inclines in various applications from simple graphs to complex terrain modeling.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will compute the slope of the line connecting these points. If the x-coordinates are equal, the slope is undefined (vertical line).

5. Frequently Asked Questions (FAQ)

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

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

Q3: What does a zero slope mean?
A: A zero slope indicates a horizontal line, meaning there is no vertical change as x changes.

Q4: What does an undefined slope mean?
A: An undefined slope occurs when the line is vertical, meaning there is no horizontal change (x₂ - x₁ = 0).

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 given by the derivative.