Finding Line Equations from Two Points and More: Easy Steps for Kids

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Megan Collins

22/01/2023

Maths

Equation of a Straight Line

Subjects

Maths

Algebra

Straight line graphs

Finding Line Equations from Two Points and More: Easy Steps for Kids

Name: Knowunity
Brand: Knowunity

This linear equation guide covers essential concepts for finding the equation of a straight line through given points and calculating gradient and y-intercept for linear equations. It provides step-by-step instructions and examples to help students master these fundamental algebraic skills.

• The guide explains how to determine the equation of a straight line using coordinates and gradient.
• It demonstrates methods for calculating gradient and y-intercept from given points or equations.
• The concept of function notation is introduced, showing how to solve linear equations using this approach.
• Various examples illustrate different scenarios and problem-solving techniques for linear equations.

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22/01/2023

333

Equation of a Straight line
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Advanced Linear Equation Concepts

This page delves deeper into linear equations, focusing on extracting information from given equations and introducing function notation. It provides examples of how to find the equation of a line on a graph and how to interpret linear equations in different forms.

The content demonstrates how to identify the gradient and y-intercept from equations in various forms, including those that are not immediately in slope-intercept form. For instance, it shows how to transform 2x + y = 13 into y = -2x + 13, revealing a gradient of -2 and a y-intercept of 13.

Example: For the equation 2x + 5y = 6, the page illustrates the process of rearranging it to find that the gradient is -2/5 and the y-intercept is 6/5.

The document introduces function notation, explaining how f $x$ = mx + c is equivalent to y = mx + c. This concept is crucial for more advanced mathematical topics and problem-solving.

Definition: Function notation f $x$ represents the output value of a function for a given input x. In linear equations, f $x$ is equivalent to y in the equation y = mx + c.

Example: If f $x$ = 4x + 1, then f $3$ = 4 $3$ + 1 = 13. This demonstrates how to evaluate a function for a specific x-value.

The page concludes with practice problems involving function notation, reinforcing the connection between linear equations and their functional representations.

Highlight: Mastering function notation is essential for students progressing to more complex mathematical concepts and for those preparing for advanced mathematics courses.

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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.

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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

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Subjects

Maths

Algebra

Straight line graphs

Maths

•

333

•

22 Jan 2023

•

2 pages

Finding Line Equations from Two Points and More: Easy Steps for Kids

Megan Collins

@megancollins

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Advanced Linear Equation Concepts

Example: For the equation 2x + 5y = 6, the page illustrates the process of rearranging it to find that the gradient is -2/5 and the y-intercept is 6/5.

The document introduces function notation, explaining how f $x$ = mx + c is equivalent to y = mx + c. This concept is crucial for more advanced mathematical topics and problem-solving.

Definition: Function notation f $x$ represents the output value of a function for a given input x. In linear equations, f $x$ is equivalent to y in the equation y = mx + c.

Example: If f $x$ = 4x + 1, then f $3$ = 4 $3$ + 1 = 13. This demonstrates how to evaluate a function for a specific x-value.

The page concludes with practice problems involving function notation, reinforcing the connection between linear equations and their functional representations.

Highlight: Mastering function notation is essential for students progressing to more complex mathematical concepts and for those preparing for advanced mathematics courses.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Equation of a Straight Line

This page introduces the fundamental concepts of linear equations and provides methods for finding the equation of a line given two points. The content focuses on the slope-intercept form of a line equation, y = mx + c, where m represents the gradient and c is the y-intercept.

Definition: The equation of a straight line in slope-intercept form is y = mx + c, where m is the gradient $slope$ and c is the y-intercept.

The page demonstrates how to calculate the gradient using the formula for gradient of a line with two points: m = $y₂ - y₁$ / $x₂ - x₁$ . This formula is essential for determining the slope of a line when given two points on that line.

Example: To find the equation of a line passing through $4,1$ with a gradient of 3, the process involves using the point-slope form: y - y₁ = m $x - x₁$ . Substituting the values gives y - 1 = 3 $x - 4$ , which simplifies to y = 3x - 11.

The document also covers how to find the equation of a line given two points, such as A $-2, 0$ and B $1, 6$ . It walks through the process of calculating the gradient and determining the y-intercept to form the complete equation.

Highlight: Understanding how to derive the equation of a line from two points is crucial for graphing linear functions and solving real-world problems involving linear relationships.

Vocabulary: The y-intercept is the point where a line crosses the y-axis, typically represented as $0, c$ in the coordinate plane.

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Stefan S

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Samantha Klich

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Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

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Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

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Rohan U

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Xander S

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Elisha

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Paul T

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Finding Line Equations from Two Points and More: Easy Steps for Kids

Advanced Linear Equation Concepts

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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.

4.9+

21 M

#1

950 K+

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

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

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

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

Finding Line Equations from Two Points and More: Easy Steps for Kids

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Advanced Linear Equation Concepts

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Equation of a Straight Line

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