Write An Equation In Slope Intercept Form Perpendicular Calculator

Perpendicular Line Equation:

\[ y = m_{\perp} x + b \] \[ \text{where } m_{\perp} = -\frac{1}{m} \]

Perpendicular Line Equation:

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1. What is the Perpendicular Line Equation?

The perpendicular line equation calculates the equation of a line that is perpendicular to a given line and passes through a specific point. Two lines are perpendicular if the product of their slopes equals -1.

2. How Does the Calculator Work?

The calculator uses the perpendicular line equation:

\[ y = m_{\perp} x + b \] \[ \text{where } m_{\perp} = -\frac{1}{m} \]

Where:

\( m_{\perp} \) — Perpendicular slope (unitless)
\( m \) — Original slope (unitless)
\( x \) — X coordinate of the point (unitless)
\( y \) — Y coordinate of the point (unitless)
\( b \) — Y-intercept (unitless)

Explanation: The perpendicular slope is the negative reciprocal of the original slope. The y-intercept is calculated using the point-slope form.

3. Importance of Perpendicular Lines

Details: Perpendicular lines are fundamental in geometry and have many practical applications in construction, engineering, and computer graphics where right angles and orthogonal relationships are required.

4. Using the Calculator

Tips: Enter the original slope and the coordinates of the point the perpendicular line must pass through. The original slope cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if the original slope is zero?
A: If the original slope is zero (horizontal line), the perpendicular line would be vertical with an undefined slope, which cannot be represented in slope-intercept form.

Q2: What if the original slope is undefined?
A: If the original line is vertical (undefined slope), the perpendicular line would be horizontal with a slope of zero.

Q3: How accurate is the calculation?
A: The calculation is mathematically exact. The calculator provides results rounded to 4 decimal places for readability.

Q4: Can I use this for 3D perpendicular lines?
A: No, this calculator is designed for 2D coordinate geometry. Perpendicular lines in 3D require vector calculations.

Q5: What are common applications of perpendicular lines?
A: Perpendicular lines are used in construction (right angles), coordinate geometry, computer graphics, and various engineering applications where orthogonal relationships are needed.