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17Calculus Precalculus - Parallel Lines

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Parallel Lines

When two lines are parallel, their slopes are equal. So, for two lines in slope intercept form \(y = mx + b_1\) and \( y=mx + b_2 \), the slopes \(m\) are the same but \( b_1 \neq b_2 \) (unless of course they are the same line). One of the nice things about the slope intercept form, \(y = mx + b\) is that you can pull the slope \(m\) and the y-intercept \(b\) directly from the equation without having to do any work. For the two parallel lines, the slopes are the same but they cross the y-axis at different points.

Okay, let's watch a great video on parallel and perpendicular lines.

Finding Equations of Parallel and Perpendicular Lines

Okay, time for some practice problems.

Practice

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

line: \( 3x-y/4 = 2 \) point: \((1/6,-8)\)

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to \( 3x-y/4 = 2 \) going through the point \((1/6,-8)\).

Final Answer

\(y=12x-10\)

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to \( 3x-y/4 = 2 \) going through the point \((1/6,-8)\).

Solution

2720 video solution

Final Answer

\(y=12x-10\)

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

Problem Statement

Write the equation of the line that is parallel to \( x - 2y = 6 \) and passes through the point \( (-4, 3) \), giving your answer in slope-intercept form.

Final Answer

\( y = x/2 + 5 \)

Problem Statement

Write the equation of the line that is parallel to \( x - 2y = 6 \) and passes through the point \( (-4, 3) \), giving your answer in slope-intercept form.

Solution

2721 video solution

Final Answer

\( y = x/2 + 5 \)

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

Problem Statement

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

Final Answer

\( y = -5x - 1 \)

Problem Statement

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

Solution

2722 video solution

Final Answer

\( y = -5x - 1 \)

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line: \( 3x+2y = 12 \) point: \( (2, -5) \)

Problem Statement

Determine the equation of the line that is parallel to \( 3x+2y = 12 \) and passes through \( (2, -5) \), giving your answer in slope-intercept form.

Final Answer

\( y = -3x/2 + 6 \)

Problem Statement

Determine the equation of the line that is parallel to \( 3x+2y = 12 \) and passes through \( (2, -5) \), giving your answer in slope-intercept form.

Solution

2723 video solution

Final Answer

\( y = -3x/2 + 6 \)

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

Problem Statement

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

Final Answer

\( y = 2x + 3 \)

Problem Statement

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

Solution

2724 video solution

Final Answer

\( y = 2x + 3 \)

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

Problem Statement

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

Final Answer

\( y = 3x - 14 \)

Problem Statement

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

Solution

2725 video solution

Final Answer

\( y = 3x - 14 \)

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

Problem Statement

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

Final Answer

\( y = 3x/2 - 9 \)

Problem Statement

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

Solution

2726 video solution

Final Answer

\( y = 3x/2 - 9 \)

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line: \( x+7y=4 \) point: \((7,9)\)

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to \( x+7y=4 \) through the point \((7,9)\).

Final Answer

\( y=-x/7+10\)

Problem Statement

Find the equation of the line, in slope-intercept form, parallel to \( x+7y=4 \) through the point \((7,9)\).

Solution

2727 video solution

Final Answer

\( y=-x/7+10\)

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Practice Instructions

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

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