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.

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 vertical change to horizontal change between two points on a line.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It describes the rate of change between variables and is essential for understanding linear relationships.

4. Using the Calculator

Tips: Enter the coordinates of two points on a line. The calculator will compute the slope. If the line is vertical (x₂ = x₁), the slope is undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line rises 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 from left to right, showing an inverse relationship between variables.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line, meaning there is no change in the y-value as x changes.

Q4: When is slope undefined?
A: Slope is undefined when the line is vertical (x₂ = x₁), as division by zero is mathematically undefined.

Q5: Can slope be used for non-linear functions?
A: The slope formula specifically calculates the slope of a straight line. For non-linear functions, we calculate the slope at a specific point using derivatives.