1. What is Slope?

Slope measures the steepness or incline of a line, calculated as the ratio of vertical change (rise) to horizontal change (run) between two points on the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( \text{Rise} \) — Vertical change between two points
• \( \text{Run} \) — Horizontal change between two points

Explanation: The slope represents how much the y-value changes for a unit change in the x-value. A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and geography. It's used in road design, roof pitch, wheelchair ramps, and analyzing data trends.

4. Using the Calculator

Tips: Enter the rise and run values in the same units. The run must be non-zero. The result is a dimensionless ratio.

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 1 mean?
A: A slope of 1 means a 45° angle where rise equals run (1 unit up for every 1 unit right).

Q2: What's the difference between slope and gradient?
A: In mathematics, they're often interchangeable, but gradient can sometimes refer to the steepness of a physical feature while slope is the mathematical ratio.

Q3: Can slope be negative?
A: Yes, negative slope means the line decreases as you move from left to right.

Q4: What's considered a steep slope?
A: In practical terms, slopes greater than 1 (45°) are considered steep, while slopes between 0 and 1 are gradual.

Q5: How is slope used in real life?
A: Slope calculations are used in construction (ramps, roofs), road design, wheelchair accessibility, hiking trail ratings, and more.