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.Table 2.Graph 3.Equation 4.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

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 FacesHow do you know if they are linear?