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
• \( (x_1, y_1) \) — 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.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It describes 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 on a line. The calculator will compute the slope. If the points have the same x-coordinate, the slope is undefined (vertical line).

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line rises as it moves from left to right.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line falls as it moves from left to right.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line with no vertical change.

Q4: Why is slope undefined for vertical lines?
A: Slope is undefined for vertical lines because 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 compute the slope accurately.