Linear Equations Perpendicular Line

Introduction to linear equations perpendicular line:

Linear equations perpendicular lines mean we are going to write the perpendicular line equation for the given line equation. Normally a linear equation is like y = mx + c. if we want to write the equation of the perpendicular line we have to calculate the slope. The slope of the perpendicular line is (-1 / m). From this we can calculate the linear equations of the perpendicular lines.

Example Problems for Linear Equations Perpendicular Lines:

Example 1 for linear equations perpendicular lines:

The slope of the line 1 is 5 and the y intercept is 20. Write the linear equation for the perpendicular line which is passes through the point (5, 2).

Solution:

Slope of the line 1is 5 and y intercept is 20.

So the equation of the line is y = 5x + 20

Perpendicular line:

The slope of the perpendicular line m2 = `- (1 / 5)` = -`1/5`

So m2 = `-1 / 5`

Equation of the perpendicular line is = `(-1 / m)` x + c

So the linear equation is y = - `(1 / 5)` x + c

This is passing through the point (5, 2)

So (2) = -`(1/ 5)` (5) + c

2 = -1 + c

C = 2 + 1 = 3

So the equation of the perpendicular line is y = -`(1 /5)` x + 3

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Example 2 for Linear Equations Perpendicular Lines:

The slope of the line 1 is 4 and the y intercept is 2. Write the linear equation for the perpendicular line which is passes through the point (1, 2).

Solution:

Slope of the line 1is 4 and y intercept is 2.

So the equation of the line is y = 4x + 2

Perpendicular line linear equation:

The slope of the perpendicular line m2 = `- (1 / 4) = -1/4`

So m2 =` -1 / 4`

Equation of the perpendicular line is = `(-1 / m)` x + c

So the linear equation is y = `- (1 / 4)` x + c

This is passing through the point (1, 2)

So (2) =` -(1/4) ` (1) + c

2 = `-1 / 4` + c

C = 2 + `1 / 4` = `9 / 4`

So the equation of the perpendicular line is y = `-(1 /4)x + (9 / 4)`

These are some of the examples for linear equations perpendicular lines.