1. What is Slope?

Slope is a measure of the steepness of a line, representing the ratio of the vertical change to the horizontal change between two points on the line. In mathematics, it's often denoted by the letter 'm'.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( \theta \) — Angle of inclination (in degrees)
• \( \tan \) — Tangent trigonometric function

Explanation: The tangent of an angle in a right triangle equals the ratio of the opposite side to the adjacent side, which corresponds to the slope of the line.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and many other fields. It's used in graphing linear equations, calculating gradients, designing roads and ramps, and analyzing rates of change.

4. Using the Calculator

Tips: Enter the angle in degrees (0-90 for positive slope, 90-180 for negative slope). The calculator will compute the tangent of the angle, which equals the slope.

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 1 mean?
A: A slope of 1 means the line rises 1 unit for every 1 unit of horizontal distance (45° angle).

Q2: What's the difference between positive and negative slope?
A: Positive slope rises to the right, negative slope falls to the right (angles between 0-90° and 90-180° respectively).

Q3: What's the slope of a vertical line?
A: A vertical line has an undefined slope (90° angle, tan(90°) is undefined).

Q4: How is slope related to the angle?
A: The slope is equal to the tangent of the angle the line makes with the positive x-axis.

Q5: Can slope be greater than 1?
A: Yes, slopes greater than 1 indicate steeper lines (angles between 45° and 90°).