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What Makes Linear and Non-Linear Functions Different?

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J

Josue Sanchez

9/26/2023

Algebra 1

Linear Functions

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Algebra 1

What Makes Linear and Non-Linear Functions Different?

A comprehensive guide explaining the difference between linear and non-linear functions, including their characteristics, graphs, and steps to find rate of change for linear functions.

  • Linear functions demonstrate a constant rate of change, producing straight-line graphs
  • Non-linear functions show varying rates of change, resulting in curved or irregular graphs
  • Key components of linear equations include slope (m) and y-intercept (b)
  • Understanding how to identify and write linear equations is crucial for mathematical analysis
  • Tables and graphs serve as essential tools for visualizing and solving linear functions
...

9/26/2023

59

Linear/Non-Linear Functions. - Linear Functions = constant rate of change Non-linear = no constant rate of change •powers other than I on th

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Page 2: Writing Linear Equations

This page details how to write linear equations with examples through a systematic three-step approach. The content breaks down the process of creating linear equations from real-world scenarios.

Definition: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope rateofchangerate of change and b represents the y-intercept initialvalueinitial value.

Example: Using a cost scenario with an initial value of 100andarateofchangeof100 and a rate of change of 75, the resulting equation would be y = 75x + 100.

Highlight: The steps to find rate of change for linear functions include:

  1. Calculate the rate of change slopeslope
  2. Identify the initial value y−intercepty-intercept
  3. Combine these elements into the equation format

Vocabulary: Rise/run refers to the method of calculating slope by dividing the vertical change by the horizontal change.

Linear/Non-Linear Functions. - Linear Functions = constant rate of change Non-linear = no constant rate of change •powers other than I on th

View

Page 3: Working with Tables and Formulas

This page demonstrates the practical application of linear equations using tables and provides detailed examples of solving linear function problems.

Example: Using the formula y = mx + b to solve for b:

  • Given equation: y = 15x + b
  • Substituting values: 35 = 1511 + b
  • Solving for b: 20 = b

Highlight: When working with tables, it's crucial to:

  • Identify patterns in the data
  • Calculate the rate of change between points
  • Determine the initial value
  • Verify the equation using multiple data points

Vocabulary: Initial value represents the starting point or y-intercept in a linear function.

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Subjects

Algebra 1

 

Algebra 1

•

59

•

Jul 7, 2025

•

3 pages

What Makes Linear and Non-Linear Functions Different?

J

Josue Sanchez

@jsanchez3075

A comprehensive guide explaining the difference between linear and non-linear functions, including their characteristics, graphs, and steps to find rate of change for linear functions.

  • Linear functions demonstrate a constant rate of change, producing straight-line graphs
  • Non-linear functions... Show more

Linear/Non-Linear Functions. - Linear Functions = constant rate of change Non-linear = no constant rate of change •powers other than I on th

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Page 2: Writing Linear Equations

This page details how to write linear equations with examples through a systematic three-step approach. The content breaks down the process of creating linear equations from real-world scenarios.

Definition: The slope-intercept form of a linear equation is y = mx + b, where m represents the slope rateofchangerate of change and b represents the y-intercept initialvalueinitial value.

Example: Using a cost scenario with an initial value of 100andarateofchangeof100 and a rate of change of 75, the resulting equation would be y = 75x + 100.

Highlight: The steps to find rate of change for linear functions include:

  1. Calculate the rate of change slopeslope
  2. Identify the initial value y−intercepty-intercept
  3. Combine these elements into the equation format

Vocabulary: Rise/run refers to the method of calculating slope by dividing the vertical change by the horizontal change.

Linear/Non-Linear Functions. - Linear Functions = constant rate of change Non-linear = no constant rate of change •powers other than I on th

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Working with Tables and Formulas

This page demonstrates the practical application of linear equations using tables and provides detailed examples of solving linear function problems.

Example: Using the formula y = mx + b to solve for b:

  • Given equation: y = 15x + b
  • Substituting values: 35 = 1511 + b
  • Solving for b: 20 = b

Highlight: When working with tables, it's crucial to:

  • Identify patterns in the data
  • Calculate the rate of change between points
  • Determine the initial value
  • Verify the equation using multiple data points

Vocabulary: Initial value represents the starting point or y-intercept in a linear function.

Linear/Non-Linear Functions. - Linear Functions = constant rate of change Non-linear = no constant rate of change •powers other than I on th

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

Page 1: Understanding Linear and Non-Linear Functions

This page introduces the fundamental distinctions between linear and non-linear functions through visual representations and key characteristics. The content focuses on helping students identify and differentiate between these function types.

Definition: Linear functions maintain a constant rate of change, while non-linear functions have varying rates of change.

Example: Linear graphs form straight lines, while non-linear graphs can be curved or irregular.

Highlight: Non-linear functions can be identified by:

  • Powers other than 1 on variables
  • Square or cube roots of variable expressions
  • Variables in denominators of fractions

Vocabulary: Rate of change refers to how much the dependent variable changes in relation to the independent variable.

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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

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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

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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

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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

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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

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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

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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