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. 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
• \( x_1, y_1 \) — 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 change in the x-value between two points.

3. Importance Of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and economics. It's used to describe rates of change, gradients, and inclines in various applications from graphing linear equations to designing roads and analyzing data trends.

4. Using The Calculator

Tips: Enter the coordinates of two distinct points. The x-coordinates must be different to calculate a defined slope. 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 as it moves from left to right. The y-values increase as the x-values increase.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line falls as it moves from left to right. The y-values decrease as the x-values increase.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line. There is no vertical change as the x-value changes.

Q4: When is slope undefined?
A: Slope is undefined when the line is vertical (x₁ = x₂). This represents an infinite slope where there is no horizontal change.

Q5: Can slope be calculated with decimal coordinates?
A: Yes, the calculator accepts decimal coordinates and will calculate the slope with precision.