1. What is Slope?

Slope is a measure of the steepness of a line, representing the ratio of vertical change to horizontal change between two points on the line. It's a fundamental concept in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses two methods to calculate slope:

Where:

• \( \theta \) — Angle of elevation in degrees
• \( (x_1, y_1) \) — Coordinates of first point
• \( (x_2, y_2) \) — Coordinates of second point

Explanation: The calculator can compute slope either from the angle of elevation using trigonometric functions, or from two points using the difference in their coordinates.

3. Importance of Slope Calculation

Details: Slope calculations are essential in various applications including road construction, roof pitch determination, wheelchair ramp design, and many engineering calculations.

4. Using the Calculator

Tips: You can either enter the angle of elevation (0-90 degrees) OR two distinct points (x₁,y₁) and (x₂,y₂). The calculator will compute both the slope and corresponding angle.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between slope and angle of elevation?
A: Slope is a ratio (rise over run) while angle of elevation is the angle between the line and the horizontal axis. They are mathematically related through the tangent function.

Q2: What does a slope of 1 mean?
A: A slope of 1 means a 45° angle, where the vertical and horizontal changes are equal (rise = run).

Q3: Can slope be negative?
A: Yes, negative slope indicates the line is decreasing as you move from left to right. Angle of elevation is always between 0-90°.

Q4: What's the maximum possible slope?
A: Theoretically infinite (for a vertical line). The angle approaches 90° as the slope increases.

Q5: How accurate is this calculator?
A: The calculator provides results with 4 decimal places for slope and 2 decimal places for angles, suitable for most practical applications.