1. What is Slope?

Slope is a measure of the steepness or incline of a line, representing the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

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

Explanation: The formula calculates the ratio of vertical change to horizontal change between two points, representing the rate of change along the line.

3. Importance of Slope Calculation

Details: Slope calculation is fundamental in mathematics, engineering, architecture, and geography. It helps determine angles of inclination, gradients, and rates of change in various applications from road construction to data analysis.

4. Using the Calculator

Tips: Enter the coordinates of two points (x1, y1) and (x2, y2). The calculator will compute the slope and express it as both a decimal value and percentage. Note that x1 and x2 cannot be equal (which would create a vertical line with undefined slope).

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, showing a positive relationship between variables.

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

Q3: What is a zero slope?
A: A zero slope indicates a horizontal line, where there is no vertical change between points.

Q4: Why is slope undefined for vertical lines?
A: Slope is undefined for vertical lines because the denominator (x2 - x1) becomes zero, and division by zero is undefined in mathematics.

Q5: How is slope percentage calculated?
A: Slope percentage is calculated by multiplying the slope value by 100. A 100% slope represents a 45-degree angle.