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10/6/2023
Algebra 1
Intercepts & Slopes
326
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Oct 6, 2023
•
Maania
@manhamaania
This document provides an in-depth explanation of slope, intercepts, and... Show more
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This page delves deeper into calculating slope using various representations of linear relationships, including graphs, tables, and equations.
The page presents a comprehensive example that demonstrates how to find the slope using three different methods:
Example: In the equation x - 2y = 3, the slope can be found by rearranging it to slope-intercept form: y = (1/2)x - (3/2).
The document emphasizes the importance of understanding how to convert between different forms of linear equations to find the slope.
Highlight: When working with equations, it's crucial to isolate the y variable to identify the slope coefficient.
The page also includes a brief introduction to the concept of y-intercept in the context of the slope-intercept form (y = mx + b).
This page focuses on the concept of intercepts in linear equations and how to find them. It explains both x-intercepts and y-intercepts and their significance in graphing linear functions.
Definition: The x-intercept is the point where a line crosses the x-axis, while the y-intercept is where it crosses the y-axis.
The page provides a step-by-step guide on how to find intercepts:
Example: For the equation y = -x + 12, the x-intercept is found by solving 0 = -x + 12, which gives x = 12. The y-intercept is found by plugging in x = 0, which gives y = 12.
The document also includes a graphical representation of intercepts and explains how to interpret them on a coordinate plane.
Highlight: The y-intercept in the slope-intercept form (y = mx + b) is represented by the constant term b.
The page concludes with a practice problem demonstrating how to find the y-intercept algebraically when given a point on the line and its slope.
This page introduces the point-slope form of linear equations, explaining its structure and how to use it to write equations of lines.
Definition: The point-slope form of a linear equation is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
The document outlines the components of the point-slope form and explains how it relates to the concept of slope as a rate of change.
Highlight: The point-slope form is particularly useful when you know the slope of a line and a point through which it passes.
The page provides several examples of how to use the point-slope form to write equations of lines, given different sets of information:
Example: Given the point (-1, 3) and slope -5, the point-slope form equation would be y - 3 = -5(x + 1).
The document also includes practice problems that demonstrate how to manipulate equations in point-slope form and how to find the slope given two points on a line.
This final page covers the standard form of linear equations and provides practice in converting between different forms of linear equations.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is non-negative.
The page outlines the characteristics of standard form and provides examples of how to convert equations from other forms into standard form.
Highlight: In standard form, x and y terms are on one side of the equation, separated from the constant term.
The document includes several practice problems that involve:
Example: Given the points (3, 9) and (1, 1), the slope is calculated as (9-1)/(3-1) = 4, and the resulting equation in slope-intercept form is y = 4x - 3.
The page concludes with more complex examples, including equations involving square roots, demonstrating the versatility of these conversion techniques in solving slope and intercept practice problems.
Vocabulary: The point-slope form can be particularly useful when dealing with point slope form equation examples with solutions.
This page introduces the concept of slope and its significance in mathematics. It covers various methods to calculate slope and introduces different forms of linear equations.
Definition: Slope measures the rate of change in a linear function.
The page outlines several ways to find slope:
Vocabulary: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
The document also explains the characteristics of positive and negative slopes, as well as special cases like horizontal and vertical lines.
Highlight: The slope of any horizontal line is 0, while the slope of any vertical line is undefined.
Examples of y-intercepts are provided, which are points where a line crosses the y-axis, such as (0,8), (0,10), and (0,31).
Example: In a graph with a negative slope, if the line goes down 2 units for every 1 unit to the right, the slope would be -2.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Maania
@manhamaania
This document provides an in-depth explanation of slope, intercepts, and various forms of linear equations, aimed at young students learning algebra and geometry. It covers key concepts and provides examples to illustrate these mathematical principles.
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Join milions of students
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This page delves deeper into calculating slope using various representations of linear relationships, including graphs, tables, and equations.
The page presents a comprehensive example that demonstrates how to find the slope using three different methods:
Example: In the equation x - 2y = 3, the slope can be found by rearranging it to slope-intercept form: y = (1/2)x - (3/2).
The document emphasizes the importance of understanding how to convert between different forms of linear equations to find the slope.
Highlight: When working with equations, it's crucial to isolate the y variable to identify the slope coefficient.
The page also includes a brief introduction to the concept of y-intercept in the context of the slope-intercept form (y = mx + b).
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page focuses on the concept of intercepts in linear equations and how to find them. It explains both x-intercepts and y-intercepts and their significance in graphing linear functions.
Definition: The x-intercept is the point where a line crosses the x-axis, while the y-intercept is where it crosses the y-axis.
The page provides a step-by-step guide on how to find intercepts:
Example: For the equation y = -x + 12, the x-intercept is found by solving 0 = -x + 12, which gives x = 12. The y-intercept is found by plugging in x = 0, which gives y = 12.
The document also includes a graphical representation of intercepts and explains how to interpret them on a coordinate plane.
Highlight: The y-intercept in the slope-intercept form (y = mx + b) is represented by the constant term b.
The page concludes with a practice problem demonstrating how to find the y-intercept algebraically when given a point on the line and its slope.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the point-slope form of linear equations, explaining its structure and how to use it to write equations of lines.
Definition: The point-slope form of a linear equation is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
The document outlines the components of the point-slope form and explains how it relates to the concept of slope as a rate of change.
Highlight: The point-slope form is particularly useful when you know the slope of a line and a point through which it passes.
The page provides several examples of how to use the point-slope form to write equations of lines, given different sets of information:
Example: Given the point (-1, 3) and slope -5, the point-slope form equation would be y - 3 = -5(x + 1).
The document also includes practice problems that demonstrate how to manipulate equations in point-slope form and how to find the slope given two points on a line.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This final page covers the standard form of linear equations and provides practice in converting between different forms of linear equations.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is non-negative.
The page outlines the characteristics of standard form and provides examples of how to convert equations from other forms into standard form.
Highlight: In standard form, x and y terms are on one side of the equation, separated from the constant term.
The document includes several practice problems that involve:
Example: Given the points (3, 9) and (1, 1), the slope is calculated as (9-1)/(3-1) = 4, and the resulting equation in slope-intercept form is y = 4x - 3.
The page concludes with more complex examples, including equations involving square roots, demonstrating the versatility of these conversion techniques in solving slope and intercept practice problems.
Vocabulary: The point-slope form can be particularly useful when dealing with point slope form equation examples with solutions.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page introduces the concept of slope and its significance in mathematics. It covers various methods to calculate slope and introduces different forms of linear equations.
Definition: Slope measures the rate of change in a linear function.
The page outlines several ways to find slope:
Vocabulary: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
The document also explains the characteristics of positive and negative slopes, as well as special cases like horizontal and vertical lines.
Highlight: The slope of any horizontal line is 0, while the slope of any vertical line is undefined.
Examples of y-intercepts are provided, which are points where a line crosses the y-axis, such as (0,8), (0,10), and (0,31).
Example: In a graph with a negative slope, if the line goes down 2 units for every 1 unit to the right, the slope would be -2.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
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
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
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
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
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 app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
