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17Calculus Precalculus - Perpendicular Lines

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Perpendicular Lines

In the case of perpendicular lines, if the equation of one line is \(y = mx + b_1\), the equation of the other is \(y=-x/m+b_2\) So the slope of the second line is said to be the negative reciprocal of the first line.

Be careful here. There is a tendency to think that if you are given the equation of the first line as \(y = mx + b_1\), to get the equation of ANY perpendicular line you just replace the slope with the negative reciprocal, i.e. \( m \to -1/m \). However, this doesn't work in all cases since the y-intercept will most likely be different. So you need to take into account that \( b_1 \neq b_2 \) most of the time and you need calculate \(b_2\). Working practice problems will help you understand this.

Practice

Unless otherwise instructed, find the equation of the line, in slope-intercept form, perpendicular to the given line going through the given point.

line: \( 9x+12y=2 \) point: \((15,7)\)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( 9x+12y=2 \) containing the point \((15,7)\).

Final Answer

\( y=4x/3 - 13 \)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( 9x+12y=2 \) containing the point \((15,7)\).

Solution

2728 video solution

Final Answer

\( y=4x/3 - 13 \)

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line: \(10x+2y=9\) point: \((20,3)\)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \(10x+2y=9\) going through the point \((20,3)\).

Final Answer

\( y = x/5 - 1 \)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \(10x+2y=9\) going through the point \((20,3)\).

Solution

2729 video solution

Final Answer

\( y = x/5 - 1 \)

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line: \( x - 4y = 15 \) point: \( (3, 1) \)

Problem Statement

Determine the equation of the line that is perpendicular to \( x - 4y = 15 \) and passes through \( (3, 1) \), giving your answer in slope-intercept form.

Final Answer

\( y = -4x + 13 \)

Problem Statement

Determine the equation of the line that is perpendicular to \( x - 4y = 15 \) and passes through \( (3, 1) \), giving your answer in slope-intercept form.

Solution

2730 video solution

Final Answer

\( y = -4x + 13 \)

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line: \( y = -3x + 2 \) point: \( (3, 5) \)

Problem Statement

Write the equation of the line that contains the point \( (3, 5) \) and is perpendicular to the line \( y = -3x + 2 \), giving your answer in slope-intercept form.

Final Answer

\( y = x/3 + 4 \)

Problem Statement

Write the equation of the line that contains the point \( (3, 5) \) and is perpendicular to the line \( y = -3x + 2 \), giving your answer in slope-intercept form.

Solution

2731 video solution

Final Answer

\( y = x/3 + 4 \)

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line: \( y = 2x + 1 \) point: \( (-4, 5) \)

Problem Statement

Determine the equation of the line that is perpendicular to \( y = 2x + 1 \) and passes through \( (-4, 5) \), giving your answer in slope-intercept form.

Final Answer

\( y = -x/2 + 3 \)

Problem Statement

Determine the equation of the line that is perpendicular to \( y = 2x + 1 \) and passes through \( (-4, 5) \), giving your answer in slope-intercept form.

Solution

2732 video solution

Final Answer

\( y = -x/2 + 3 \)

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line: \( y = 5x - 3 \) point: \( (2, -1) \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = 5x - 3 \) that passes through the point \( (2, -1) \), giving your answer in slope-intercept form.

Final Answer

\( y = -x/5 - 3/5 \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = 5x - 3 \) that passes through the point \( (2, -1) \), giving your answer in slope-intercept form.

Solution

2733 video solution

Final Answer

\( y = -x/5 - 3/5 \)

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line: \( y = 3x/4 - 1 \) point: \( (8, -3) \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = 3x/4 - 1 \) that passes through the point \( (8, -3) \), giving your answer in slope-intercept form.

Final Answer

\( y = -4x/3 + 23/3 \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = 3x/4 - 1 \) that passes through the point \( (8, -3) \), giving your answer in slope-intercept form.

Solution

2734 video solution

Final Answer

\( y = -4x/3 + 23/3 \)

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line: \( y = -2x/3 + 4 \) point: \( (6, -2) \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = -2x/3 + 4 \) that passes through the point \( (6, -2) \), giving your answer in slope-intercept form.

Final Answer

\( y = 3x/2 - 11 \)

Problem Statement

Find the equation of the line perpendicular to the line \( y = -2x/3 + 4 \) that passes through the point \( (6, -2) \), giving your answer in slope-intercept form.

Solution

2735 video solution

Final Answer

\( y = 3x/2 - 11 \)

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line: \( y=2x+1 \) point: \((2,0)\).

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( y=2x+1 \) through the point \((2,0)\).

Final Answer

\( y = -x/2 + 1 \)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( y=2x+1 \) through the point \((2,0)\).

Solution

2736 video solution

Final Answer

\( y = -x/2 + 1 \)

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line: \( y=-9x+5 \) point: \((3,9)\)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( y=-9x+5 \) through the point \((3,9)\).

Final Answer

\( y = x/9 + 26/3 \)

Problem Statement

Find the equation of the line, in slope-intercept form, perpendicular to \( y=-9x+5 \) through the point \((3,9)\).

Solution

2737 video solution

Final Answer

\( y = x/9 + 26/3 \)

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Practice Instructions

Unless otherwise instructed, find the equation of the line, in slope-intercept form, perpendicular to the given line going through the given point.

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