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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?