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Y = mx + c

Understanding Lines: Midpoints, Equations, and Cool Tricks

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Sahal Hassan

@sahalh_g

·

20 Followers

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Subject Expert

18/11/2022

176

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Page 2: Midpoint Calculations and Line Properties

This page delves into midpoint calculations and more complex line properties, including perpendicular lines and distance calculations.

Definition: The midpoint formula is used to find the center point between two coordinates: (x₁+x₂)/2, (y₁+y₂)/2

Example: A detailed calculation shows finding coordinates of point B(5,8) using gradient relationships.

Highlight: The negative reciprocal relationship between perpendicular lines is demonstrated through practical examples.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

View

Page 3: Axis Intersections and Distance Calculations

The content focuses on finding where lines intersect with axes and calculating distances between points using the distance formula.

Definition: The distance formula between two points is √((x₂-x₁)² + (y₂-y₁)²)

Example: Finding intersection points A(0,8) and B(-12,0) with the axes.

Highlight: The midpoint calculation (-6,4) is shown as an important step in solving geometric problems.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

View

Page 4: Complex Line Relationships

This page covers more advanced concepts involving multiple lines and their relationships, including perpendicular lines and intersection points.

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

Example: Solving systems of equations to find intersection points.

Highlight: The transformation of equations from general form to slope-intercept form is demonstrated.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

View

Page 4: Complex Line Problems

This section covers more advanced problems involving multiple lines and their relationships.

Example: Solving systems of equations to find intersection points of two lines.

Definition: Two lines are perpendicular if their gradients are negative reciprocals of each other.

Highlight: When converting between different forms of line equations, it's crucial to maintain the same mathematical relationship while changing the presentation.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

View

Page 1: Linear Equations and Gradients

This page introduces fundamental concepts of linear equations and gradient calculations. The content focuses on working with different forms of linear equations and understanding the relationship between lines.

Definition: The point-slope form of a line is y - y₁ = m(x - x₁), where m is the gradient and (x₁,y₁) is a point on the line.

Example: A gradient calculation is shown where m = (y₂-y₁)/(x₂-x₁) = -3

Highlight: The relationship between perpendicular lines is demonstrated through their negative reciprocal gradients.

Vocabulary: Gradient (m) represents the slope or steepness of a line.

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

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Knowunity is the #1 education app in five European countries

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I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

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The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Generate Summary

Subjects

/

Maths

/

Algebra

/

Straight line graphs

/

Y = mx + c

Understanding Lines: Midpoints, Equations, and Cool Tricks

user profile picture

Sahal Hassan

@sahalh_g

·

20 Followers

Follow

Understanding equations of a line in math and geometric relationships between lines forms the foundation of coordinate geometry. This comprehensive guide covers line equations, perpendicular lines, and finding midpoints.

• The guide explores various forms of linear equations including point-slope form (y - y₁ = m(x - x₁)) and standard form (ax + by + c = 0)
• Key concepts include calculating gradients, finding the midpoint of a line segment, and determining negative reciprocal for perpendicular lines
• Practical applications involve solving geometric problems with parallel and perpendicular lines
• The material emphasizes the relationship between different forms of linear equations and their geometric interpretations

18/11/2022

176

 

12/13

 

Maths

1

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Midpoint Calculations and Line Properties

This page delves into midpoint calculations and more complex line properties, including perpendicular lines and distance calculations.

Definition: The midpoint formula is used to find the center point between two coordinates: (x₁+x₂)/2, (y₁+y₂)/2

Example: A detailed calculation shows finding coordinates of point B(5,8) using gradient relationships.

Highlight: The negative reciprocal relationship between perpendicular lines is demonstrated through practical examples.

Similar content

Know Straight Line Grpahs and Equations thumbnail

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136

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Notes covering straight line graphs in KS3 Maths. Includes diagrams, definitions and examples.

Know Equation of a straight line and graphs GCSE thumbnail

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681

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Know Turning point and roots practice thumbnail

2

109

11

Maths Turning point and roots practice

Learn how to find the turning point and roots of the equation using the graph of y = -2r-3 -6.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Axis Intersections and Distance Calculations

The content focuses on finding where lines intersect with axes and calculating distances between points using the distance formula.

Definition: The distance formula between two points is √((x₂-x₁)² + (y₂-y₁)²)

Example: Finding intersection points A(0,8) and B(-12,0) with the axes.

Highlight: The midpoint calculation (-6,4) is shown as an important step in solving geometric problems.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Complex Line Relationships

This page covers more advanced concepts involving multiple lines and their relationships, including perpendicular lines and intersection points.

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

Example: Solving systems of equations to find intersection points.

Highlight: The transformation of equations from general form to slope-intercept form is demonstrated.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Complex Line Problems

This section covers more advanced problems involving multiple lines and their relationships.

Example: Solving systems of equations to find intersection points of two lines.

Definition: Two lines are perpendicular if their gradients are negative reciprocals of each other.

Highlight: When converting between different forms of line equations, it's crucial to maintain the same mathematical relationship while changing the presentation.

Thursday 17 November 2022 Chapter 5 Revision Maths Genie (The Equation of a hine) 1) y - y₁ = m ( x-x₁) m= −9-1 = − 6 = -3 4-2 2 y = c - 3 x

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Linear Equations and Gradients

This page introduces fundamental concepts of linear equations and gradient calculations. The content focuses on working with different forms of linear equations and understanding the relationship between lines.

Definition: The point-slope form of a line is y - y₁ = m(x - x₁), where m is the gradient and (x₁,y₁) is a point on the line.

Example: A gradient calculation is shown where m = (y₂-y₁)/(x₂-x₁) = -3

Highlight: The relationship between perpendicular lines is demonstrated through their negative reciprocal gradients.

Vocabulary: Gradient (m) represents the slope or steepness of a line.

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Notes covering straight line graphs in KS3 Maths. Includes diagrams, definitions and examples.

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Know Straight Line Grpahs and Equations thumbnail

Maths - Equation of a straight line and graphs GCSE

Includes y = mx + c, gradient , finding the equation of a straight line, finding the equation of the line from the graph and form points and exam style questions

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Know Equation of a Straight Line thumbnail

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National 5 Maths - Block 2 notes on topics such as changing the subject,volume, interquartile range, standard deviation, gradient, straight line and more

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Know Block 2 - National 5 Maths thumbnail

Maths - Turning point and roots practice

Learn how to find the turning point and roots of the equation using the graph of y = -2r-3 -6.

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Know Turning point and roots practice thumbnail

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

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the 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 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.