1. What is the Slope-Intercept Form?

The slope-intercept form is a linear equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is widely used in algebra and coordinate geometry to describe straight lines.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( m \) — Slope of the line (unitless)
• \( b \) — Y-intercept (unitless)
• \( x₁, y₁ \) — Coordinates of the first point
• \( x₂, y₂ \) — Coordinates of the second point

Explanation: The calculator takes two points on a line and calculates the slope and y-intercept to form the equation y = mx + b.

3. Importance of Slope-Intercept Form

Details: The slope-intercept form is fundamental in mathematics for graphing linear equations, analyzing relationships between variables, and solving systems of equations. It provides a clear visual representation of how changes in x affect y.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points on the line. The points must not have the same x-coordinate (which would result in a vertical line with undefined slope).

5. Frequently Asked Questions (FAQ)

Q1: What if the two points have the same x-coordinate?
A: If x₁ = x₂, the line is vertical and the slope is undefined. The equation cannot be written in slope-intercept form.

Q2: What does the slope value represent?
A: The slope (m) represents the rate of change of y with respect to x. A positive slope indicates an increasing line, negative slope indicates a decreasing line.

Q3: What is the y-intercept?
A: The y-intercept (b) is the point where the line crosses the y-axis (when x = 0).

Q4: Can I use this for non-linear equations?
A: No, this calculator is specifically designed for linear equations that can be expressed in the form y = mx + b.

Q5: How accurate are the results?
A: The results are mathematically exact for the given points. The calculator provides results rounded to 4 decimal places for readability.