1.3 Linear vs. Non-Linear

Linear vs. Non-Linear Relations

Learning Outcomes

Identify a linear and non-linear relationships from:

• Graphs

• Equations

• Table of Values

• Stories/Descriptions

Multiple Choice

Educated Guess: Which Graph is Linear?

Linear graphs are represented by a straight line.

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​Linear Graphs

Multiple Choice

Estimated Guess: Which Equation shows a Linear Relationship?

• $$y\ =\ x\ +\ 1$$

• $$y\ =\ x^2$$

• $$y\ =\ \sqrt[]{x}$$

• $$y\ =\ 2^x$$

The power of a variable is 1.

This means:

• No roots.

• No exponents other than 1

• x cannot be a denominator
  

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​Linear Equations

Multiple Select

Select all equations that are linear.

• $$y\ =\ 2x$$

• $$y\ =\ \frac{1}{x}$$

• $$y\ =\ \frac{x}{3}+\ 1$$

• $$y\ =\ x^4\ +\ 2$$

Multiple Choice

Educated Guess: Which Table Shows a Linear Relationship?

​The values in the table increase or decrease by the same amount each time

Linear Tables

Multiple Choice

True or False?

This table shows a linear relationship.

• True

• False

Multiple Select

Select all tables that show a linear relationship.

When a raccoon finds a full dumpster it calls three of its friends. Each of these new raccoons then call three of their friends.

Non-Linear

Deirdre earns $100 each day she works at her local clothes store. For each item of clothing she sells, she makes an extra $10.

Linear

Linear vs. Non-Linear Stories

Multiple Choice

Linear or Non-linear.

In a zombie apocalypse the first person infected bites four people and each of those zombies bites another four people.

• Linear

• Non-linear

Multiple Choice

Linear or Non-Linear?

Deirbhle is going on a long cycle. Every 20 minutes she cycles a distance of 5km.

• Linear

• Non-linear

Multiple Choice

Linear or Non-linear?

A grasshopper is jumping to the end of a meter stick. Each jump he takes is half the distance of his last jump.

• Linear

• Non-linear