What Makes Linear and Non-Linear Functions Different?

Open

Josue Sanchez

9/26/2023

Algebra 1

Linear Functions

Subjects

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

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

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 (rate of change) and b represents the y-intercept (initial value).

Example: Using a cost scenario with an initial value of $100 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:

Calculate the rate of change (slope)
Identify the initial value (y-intercept)
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.

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 = 15(1) + 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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

17 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

Algebra 1

What Makes Linear and Non-Linear Functions Different?

Josue Sanchez

@jsanchez3075

3 Followers

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

8th

Algebra 1

Sign up to see the content. It'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 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 (rate of change) and b represents the y-intercept (initial value).

Example: Using a cost scenario with an initial value of $100 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:

Calculate the rate of change (slope)
Identify the initial value (y-intercept)
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.

Sign up to see the content. It'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 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 = 15(1) + 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.

Sign up to see the content. It'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.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

17 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User