1. What is a Line Equation?

A line equation describes the relationship between x and y coordinates of all points on a straight line. The slope-intercept form (y = mx + b) is the most common representation, where m is the slope and b is the y-intercept.

2. How Does the Calculator Work?

The calculator uses these formulas:

Where:

• \( (x_1, y_1) \) — First point coordinates
• \( (x_2, y_2) \) — Second point coordinates
• \( m \) — Slope of the line
• \( b \) — Y-intercept

Explanation: The slope (m) measures the steepness of the line, while the y-intercept (b) is where the line crosses the y-axis.

3. Importance of Line Equations

Details: Line equations are fundamental in algebra and have wide applications in physics, engineering, economics, and computer graphics for modeling linear relationships.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will automatically detect vertical lines (undefined slope) and display them appropriately.

5. Frequently Asked Questions (FAQ)

Q1: What if my points create a vertical line?
A: The calculator will display "x = constant" since vertical lines have undefined slope and cannot be represented in slope-intercept form.

Q2: How accurate are the results?
A: Results are rounded to 4 decimal places for clarity while maintaining good precision.

Q3: Can I use this for horizontal lines?
A: Yes, horizontal lines will show a slope (m) of 0 (e.g., y = 0x + b).

Q4: What if my points are the same?
A: The calculator requires two distinct points to determine a unique line.

Q5: Can I find the x-intercept from this equation?
A: Yes, set y=0 and solve for x: x = -b/m (when m≠0).