This linear equation guide covers essential concepts for finding the... Show more
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
7
1
Megan Collins
22/01/2023
Maths
Equation of a Straight Line
333
•
22 Jan 2023
•
Finding Line Equations from Two Points and More: Easy Steps for Kids
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.
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.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Finding Line Equations from Two Points and More: Easy Steps for Kids
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... Show more
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.
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.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.9/5
App Store
4.8/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
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
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user