Lesson 1: Identifying Linear Relations
Module 5: Linear Functions
Lesson 1 Summary
In Lesson 1 you investigated the following questions:
-
How can you distinguish a linear relation from a non-linear relation?
-
How can the concept of slope be used to identify a linear relation?
In this lesson you learned to identify relations as linear or non-linear when they are presented as graphs, tables, and equations. There are several ways to know whether a relation is linear or not.
1. A graph can be identified as linear if the points on the graph can be connected with a single line.Sometimes the need to develop a table of values and graph for there is necessary.
2. An equation represents a linear relation if it can be written in the form y = mx + b. You can also identify an equation as a linear relation if it contains one or two variables and is a first-degree equation.
3. The slope calculated between any two data points in the table is constant. You learned previously that the slope of a line is constant. This concept also helps you to identify a linear relation. For example, the data in a table is linear if the slope calculated between any two data points in the table is constant. A set of ordered pairs is considered linear if the slope between any two ordered pairs is constant. Indeed, the constant is the slope of the linear relation.
In the next lesson you will examine linear functions. Recall that a function is a special type of relation where each input value only has one output value. You will investigate the features of linear functions such as domain, range, and intercepts.