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 To Calculate Slope

The slope formula is:

Where:

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

Explanation: The numerator represents the vertical change (difference in y-values) and the denominator represents the horizontal change (difference in x-values) between the two points.

3. Importance Of Slope Calculation

Details: Slope is a fundamental concept in mathematics, physics, engineering, and economics. It describes the rate of change between two variables and is essential for understanding linear relationships, graphing equations, and solving real-world problems involving rates.

4. Using The Calculator

Tips: Enter the coordinates of two distinct points. The x-values must be different (x₂ ≠ x₁) to avoid division by zero. The calculator will compute the slope and display the result.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line is increasing - as x increases, y also increases.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line is decreasing - as x increases, y decreases.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line, where y-values remain constant regardless of x-values.

Q4: What if the slope is undefined?
A: An undefined slope occurs when x₂ = x₁, resulting in a vertical line where the x-value remains constant.

Q5: How is slope used in real-world applications?
A: Slope is used to calculate rates such as speed (distance over time), unit cost (price per item), and many other proportional relationships in science, economics, and engineering.