Four Faces of a Linear Function

How is a linear relationship used in our everyday world?

Today we will…

Define Linear Relationship

Discuss the Four Faces of a Linear Function(How do we know that a table, graph, equation, and story problem are a linear relationship?)

Identify the rate and the beginning value of the four faces

Definition of a Linear Relationship

A linear relationship is a relationship between two things (x and y) that shows a line on a graph and it contains a constant rate of change.

Other Definitions:

Independent Variable

Dependent Variable

Rate

Beginning Value

Four Faces of a Linear Function

1. Table2. Graph3. Equation4. Story Problem

How can we see a linear relationship in each of the four faces of a function?

1. Table ~ both the independent and dependent variables will increase or decrease at a constant rate

2. Graph ~ line (Linear)

3. Equation ~ will be in the form of y = mx + b; the equation will be in the first degree

4. Story Problem ~ will contain a constant; look for the word “per” in the story problem

Table:

Both x and y Increase/Decrease at A Constant Rate

Graph:

The graph makes a straight line

Equation:

Is written in the form of

Beginning Value (y-intercept)

Story Problem

constant; Contains the word “Per”

1. A Rate: The rate is your slope (m) in the problem. Examples of Rate:

• $3 per day• $2 an hour• $5 per person• $3.50 per gallon• $6.25 a minute

The rate is always related to the x value. The rate is always next to x in the equation. 2. A Flat Fee: A flat fee is your beginning value (b) or the y-intercept.The value is not a variable. It is a single number that stands alone.

Examples of Rate: • I had $75 in my savings account to start• The initial fee to rent a trailer is $100• The cost to join the video store is $40

Story Problem

Summary

Name the 4 Faces

How do you know if they are linear?