1. What is the Slope Formula?

The slope formula calculates the steepness or incline of a line between two points in a coordinate system. It represents the rate of change between the y-values and x-values of the two points.

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 calculator accepts fractions as input, converts them to decimal values, then computes the difference in y-values divided by the difference in x-values.

3. Importance of Slope Calculation

Details: Slope calculation is fundamental in mathematics, physics, engineering, and economics. It helps determine rates of change, gradients, and linear relationships between variables.

4. Using the Calculator

Tips: Enter coordinates as fractions (e.g., 1/2, 3/4) or decimals. The calculator will compute the slope and display the result in decimal format. If the denominator is zero, it indicates a vertical line with undefined slope.

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 x and y 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 x and y variables.

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

Q5: Can I use mixed numbers as input?
A: Yes, you can enter mixed numbers as improper fractions (e.g., 1½ as 3/2) for accurate calculation.