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Linear Equations: Notes on Parallel and Perpendicular Lines

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Shardsicle

5/27/2023

Algebra 1

Linear Equations - parallel and perpendicular lines notes

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Algebra 1

Linear Equations: Notes on Parallel and Perpendicular Lines

Linear equations and parallel lines guide explains the fundamental concepts of parallel and perpendicular lines in algebraic form, with detailed examples and step-by-step solutions.

• Understanding parallel and perpendicular lines equations requires knowledge of slope relationships
• Parallel lines equation examples demonstrate that parallel lines have identical slopes
• The guide covers writing equations of parallel and perpendicular lines through given points
• Examples include converting equations to slope-intercept form for easier analysis
• Step-by-step solutions show how to find equations of parallel and perpendicular lines using points and slopes

...

5/27/2023

491

<h2 id="bigidea">Big Idea:</h2> <p>Two lines are parallel if and only if they never intersect.</p> <h2 id="writinglinearequationsofparallel

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Page 2: Advanced Examples of Parallel Lines

This page delves deeper into practical applications of writing parallel line equations and includes multiple worked examples.

Example: Writing an equation through point (-2,11) parallel to y = -x + 5:

  • Identify slope: m = -1
  • Use point-slope form
  • Final equation: y = -x + 9

Highlight: Converting equations to slope-intercept form makes identifying slopes easier.

Definition: Perpendicular lines have slopes that are negative reciprocals of each other.

Example: For a line perpendicular to y = 2x - 3 through (4,-5):

  • Original slope: m = 2
  • Perpendicular slope: m = -1/2
  • Final equation: y = -1/2x - 3
<h2 id="bigidea">Big Idea:</h2> <p>Two lines are parallel if and only if they never intersect.</p> <h2 id="writinglinearequationsofparallel

View

Page 3: Complex Applications and Line Relationships

The final page explores more complex examples and relationships between multiple lines.

Example: Analysis of three lines to determine parallel and perpendicular relationships:

  • Line a: y = 5x - 3
  • Line b: x + 5y = 2
  • Line c: -10y - 2x = 0

Highlight: When comparing multiple lines, convert all equations to slope-intercept form first.

Definition: Lines are perpendicular if their slopes are negative reciprocals of each other.

Example: Converting complex equations:

  • x + 5y = 2 becomes y = -1/5x + 2/5
  • -10y - 2x = 0 becomes y = -1/5x

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Algebra 1

Linear Equations: Notes on Parallel and Perpendicular Lines

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Shardsicle

@shardsicle_fazn

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Linear equations and parallel lines guide explains the fundamental concepts of parallel and perpendicular lines in algebraic form, with detailed examples and step-by-step solutions.

• Understanding parallel and perpendicular lines equations requires knowledge of slope relationships
• Parallel lines equation examples demonstrate that parallel lines have identical slopes
• The guide covers writing equations of parallel and perpendicular lines through given points
• Examples include converting equations to slope-intercept form for easier analysis
• Step-by-step solutions show how to find equations of parallel and perpendicular lines using points and slopes

...

5/27/2023

491

 

8th

 

Algebra 1

37

<h2 id="bigidea">Big Idea:</h2> <p>Two lines are parallel if and only if they never intersect.</p> <h2 id="writinglinearequationsofparallel

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Page 2: Advanced Examples of Parallel Lines

This page delves deeper into practical applications of writing parallel line equations and includes multiple worked examples.

Example: Writing an equation through point (-2,11) parallel to y = -x + 5:

  • Identify slope: m = -1
  • Use point-slope form
  • Final equation: y = -x + 9

Highlight: Converting equations to slope-intercept form makes identifying slopes easier.

Definition: Perpendicular lines have slopes that are negative reciprocals of each other.

Example: For a line perpendicular to y = 2x - 3 through (4,-5):

  • Original slope: m = 2
  • Perpendicular slope: m = -1/2
  • Final equation: y = -1/2x - 3
<h2 id="bigidea">Big Idea:</h2> <p>Two lines are parallel if and only if they never intersect.</p> <h2 id="writinglinearequationsofparallel

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Page 3: Complex Applications and Line Relationships

The final page explores more complex examples and relationships between multiple lines.

Example: Analysis of three lines to determine parallel and perpendicular relationships:

  • Line a: y = 5x - 3
  • Line b: x + 5y = 2
  • Line c: -10y - 2x = 0

Highlight: When comparing multiple lines, convert all equations to slope-intercept form first.

Definition: Lines are perpendicular if their slopes are negative reciprocals of each other.

Example: Converting complex equations:

  • x + 5y = 2 becomes y = -1/5x + 2/5
  • -10y - 2x = 0 becomes y = -1/5x
<h2 id="bigidea">Big Idea:</h2> <p>Two lines are parallel if and only if they never intersect.</p> <h2 id="writinglinearequationsofparallel

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Page 1: Introduction to Parallel and Perpendicular Lines

This page introduces fundamental concepts about parallel and perpendicular lines in algebra. The content focuses on the algebraic representation of these geometric relationships.

Definition: Two lines are parallel if and only if they never intersect on a graph.

Highlight: Parallel lines must have the same slope but different y-intercepts.

Example: Parallel equations demonstrated:

  • y = √3x + 5
  • y = √3x - 3

Vocabulary: Slope-intercept form (y = mx + b) is the standard form used to write linear equations.

Definition: To write equations of parallel or perpendicular lines:

  1. Identify the slope of the given line
  2. Determine the required slope for the new line
  3. Use point-slope form to write the equation

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

20 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying