1. What is the Equation of a Parallel Line?

The equation of a parallel line has the same slope as the original line but a different y-intercept. Parallel lines never intersect and maintain a constant distance between them.

2. How Does the Calculator Work?

The calculator uses the slope-intercept form:

Where:

• \( m \) — Slope of the original line (same for parallel line)
• \( b_{\text{new}} \) — New y-intercept calculated using the given point
• \( (x, y) \) — Point that the parallel line must pass through

Explanation: The calculator determines the new y-intercept by plugging the known point into the equation and solving for \( b_{\text{new}} \).

3. Importance of Parallel Lines

Details: Parallel lines are fundamental in geometry and have applications in architecture, engineering, and computer graphics where maintaining consistent spacing is crucial.

4. Using the Calculator

Tips: Enter the slope of the original line and the coordinates of a point you want the parallel line to pass through. The calculator will provide the complete equation.

5. Frequently Asked Questions (FAQ)

Q1: How do I know if two lines are parallel?
A: Two lines are parallel if they have identical slopes but different y-intercepts.

Q2: Can vertical lines be parallel?
A: Yes, all vertical lines are parallel to each other since they have undefined slopes.

Q3: What's the difference between parallel and perpendicular lines?
A: Parallel lines never intersect, while perpendicular lines intersect at right angles (90 degrees).

Q4: How many parallel lines can pass through a given point?
A: For any given line and point not on that line, there is exactly one parallel line through that point (Euclidean geometry).

Q5: Can horizontal lines be parallel?
A: Yes, all horizontal lines are parallel to each other since they have a slope of 0.