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alejandralyne0204
10/20/2023
Algebra 1
Understanding linear functions pt.2
Linear functions are fundamental mathematical concepts with constant rates of change. This guide provides a detailed explanation of linear functions with examples and answers, covering key topics like graphing, standard form, and real-world applications. Students will learn to identify, graph, and analyze linear function examples with solutions and graphs.
10/20/2023
104
This page focuses on the standard form of linear equations and provides examples of graphing linear functions.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero.
The lesson provides an example of graphing the linear equation 5x + y = 10:
Example: To determine if a point is on the graph of 5x + y = 10, substitute the values: 5 + 5 = 15 ≠ 10, so is not on the graph.
Highlight: When graphing linear functions, it's important to note that A and B in the standard form cannot be zero simultaneously.
This page covers real-world applications of linear functions and introduces graphing techniques, including using intercepts.
Example: Sal's video store pricing model is represented by the function F = 2x, where x is the number of DVDs purchased. This results in a discrete graph.
The lesson explains how to determine the domain and range of this function:
Highlight: When graphing discrete functions, use individual points rather than a continuous line.
The lesson introduces a problem about miners ascending in an elevator, which will be used to demonstrate graphing linear functions using intercepts in the next lesson.
Vocabulary: Intercepts are the points where a graph crosses the x-axis or y-axis .
This comprehensive guide provides students with a solid foundation in understanding and working with linear functions, preparing them for more advanced mathematical concepts.
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alejandralyne0204
@alejandralyne0204_xgpl
Linear functions are fundamental mathematical concepts with constant rates of change. This guide provides a detailed explanation of linear functions with examples and answers, covering key topics like graphing, standard form, and real-world applications. Students will learn to identify,... Show more
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This page focuses on the standard form of linear equations and provides examples of graphing linear functions.
Definition: The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers, and A and B are not both zero.
The lesson provides an example of graphing the linear equation 5x + y = 10:
Example: To determine if a point is on the graph of 5x + y = 10, substitute the values: 5 + 5 = 15 ≠ 10, so is not on the graph.
Highlight: When graphing linear functions, it's important to note that A and B in the standard form cannot be zero simultaneously.
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Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page covers real-world applications of linear functions and introduces graphing techniques, including using intercepts.
Example: Sal's video store pricing model is represented by the function F = 2x, where x is the number of DVDs purchased. This results in a discrete graph.
The lesson explains how to determine the domain and range of this function:
Highlight: When graphing discrete functions, use individual points rather than a continuous line.
The lesson introduces a problem about miners ascending in an elevator, which will be used to demonstrate graphing linear functions using intercepts in the next lesson.
Vocabulary: Intercepts are the points where a graph crosses the x-axis or y-axis .
This comprehensive guide provides students with a solid foundation in understanding and working with linear functions, preparing them for more advanced mathematical concepts.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Linear functions are characterized by a constant rate of change between variables. This lesson introduces the concept of linear functions, their properties, and how to distinguish them from non-linear functions.
Definition: A linear function is a mathematical relationship where a constant change in one variable corresponds to a constant change in another variable.
The lesson emphasizes that all linear functions behave similarly and can be represented by linear equations with two variables. Examples of linear equations include:
Example: The equation y = x² is not a linear function because it does not have a constant change in y for a constant change in x.
Highlight: In linear equations, the highest exponent for x and y is always 1.
The lesson also introduces non-linear equations, such as:
Vocabulary: Non-linear functions are mathematical relationships where the rate of change between variables is not constant.
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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
