Lesson 1: Identifying Linear Relations: Explore

Math 10C Module 5: Lesson 1

Module 5: Linear Functions

Explore

This shows a photo of an athlete competing in a swimming event.

A linear relation is a relation whose graph is represented by points along a straight line. On the other hand, a non-linear relation is a relation whose graph is not represented by a straight line.

This shows a graph of a linear relation (left) where the points can be joined by a single line and a graph of a non-linear relation (right) where the points cannot be joined by a single line.

For instance, you have seen in Module 4 that some distance-time graphs can be represented by straight-line graphs. You have also seen that the slopes of these graphs are constant and that they represent speed. In Olympic disciplines, where a constant speed needs to be maintained, you will find examples of a linear relationship between distance and time. Examples of such disciplines include endurance races in swimming and running.

In this lesson you will examine different representations of relations and learn how to tell if each one is a linear relation. You will also learn that examples of linear relations are not confined to distance-time graphs.

Glossary Terms

Add the following terms to your "Glossary Terms" section in your notes.

You may also want to add examples that demonstrate how each term is applied.

linear relation
non-linear relation

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Any relation whose graph is represented by a straight line is considered a linear relation.

This shows three graphs of linear relations.

Tip

Graphing a relation is a sure-fire way of finding out whether a relation is linear. If a single straight line can pass through the points on the graph, the relation is linear.

In Module 4 you learned about the slopes of lines. Slope is the measure of the steepness of a line. Slope can be thought of as

eqn001.eps

You also learned that the slope of a straight line is constant. Recall Math Lab: Slope of a Staircase in Module 4: Lesson 4, where you determined the rise/run ratio of a single step on a staircase and compared that ratio to the slope of the entire staircase.

These concepts can help you to determine whether a relation in any form is linear or nonlinear.

Try This 1 - 4

Complete the following in your binder. You can print the file or open it and just complete the questions.

Try This 1 - 4 questions

Use the link below to check your answers to Try This 1 - 4.

Possible TT1-4 (Try This 1-4) Solutions

THINK: How can you tell if a table of values represents a linear relation?

Read

Go to your textbook to confirm your response to the question above. As you read, try to find out what aspects of a table of values must be constant in order for the relation to be considered linear. Also, try to identify any exceptions. ** Write a rule for yourself on your TT1 - 4 pages**

Foundations and Pre-calculus Mathematics 10 (Pearson)

Read “Example 1: Determining Whether a Table of Values Represents a Linear Relation” on page 303.

A relation can also be represented by a set of ordered pairs. Just as there are many ways of representing a relation, there are also many strategies you can use to identify whether a relation is linear or non-linear.