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 any two points on the line. It describes both the direction and the steepness of the line.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

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

Explanation: The formula calculates how much the y-value changes for each unit of change in the x-value between two points on a line.

3. Importance of Slope Calculation

Details: Slope is a fundamental concept in mathematics, physics, engineering, and economics. It's used to describe rates of change, gradients, and inclines in various applications from graph analysis to real-world measurements.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points from your picture. The calculator will compute the slope between these points. Note that if x₁ = x₂, the line is vertical and 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, meaning as x increases, y also increases.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line falls from left to right, meaning as x increases, y decreases.

Q3: What is a zero slope?
A: A zero slope indicates a horizontal line, meaning there is no vertical change as x changes.

Q4: Why is slope undefined for vertical lines?
A: For vertical lines, the denominator (x₂ - x₁) becomes zero, and division by zero is undefined in mathematics.

Q5: Can slope be calculated with decimal coordinates?
A: Yes, the calculator accepts decimal coordinates and will provide the slope as a decimal value.