1. What Are Parallel and Perpendicular Lines?

Parallel lines are lines in a plane that never meet; they have identical slopes. Perpendicular lines intersect at right angles; their slopes are negative reciprocals of each other.

2. How Does the Calculator Work?

The calculator uses these mathematical principles:

Where:

• \( m \) — Slope of the original line
• \( m_{\perp} \) — Slope of the perpendicular line

Explanation: Given a point (x₁, y₁), the equation of a line through that point with slope m is y - y₁ = m(x - x₁).

3. Mathematical Principles

Details: For vertical lines (undefined slope), the parallel line will also be vertical, and the perpendicular line will be horizontal (slope = 0), and vice versa.

4. Using the Calculator

Tips: Enter the slope and y-intercept of your original line, plus any point you want the new lines to pass through. The calculator will find equations for both parallel and perpendicular lines through your specified point.

5. Frequently Asked Questions (FAQ)

Q1: What if my original line is horizontal?
A: A parallel line will also be horizontal (same slope = 0). The perpendicular line will be vertical (undefined slope).

Q2: What if my original line is vertical?
A: A parallel line will also be vertical. The perpendicular line will be horizontal (slope = 0).

Q3: Can I use this for 3D lines?
A: No, this calculator is for 2D lines only. 3D lines have more complex relationships.

Q4: How precise are the results?
A: Results are calculated to 2 decimal places for clarity, but use exact fractions when possible for mathematical work.

Q5: What if I get "undefined" for a slope?
A: This means the line is vertical, and its equation will be in the form x = constant.