4.4 Initial Value.notebook
April 03, 2014
Review #1
Which of the relationships represented below has a constant rate of change?
Recall
The following two companies will fix your computer if it breaks down:
Compufix charges a base fee of $50 plus $30/h for a service call.
Computer Doctor has no base fee, but charges $55/h.
Determining the Initial Value from a Description (Words)
What is the initial value for each linear relation above?
Compufix Computer Doctor
Use your own words to describe what initial value means.
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4.4 Initial Value.notebook
April 03, 2014
Determining the Initial Value from a Table of Values
Compufix
Computer Doctor
Use your own words to describe how to determine the initial value from a table of values.
Determining the Initial Value from a Graph
Compufix
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4.4 Initial Value.notebook
April 03, 2014
Computer Doctor
Use your own words to
describe how to determine
the initial value from a
graph.
Determining the Initial Value from an Equation
Compufix:
Computer Doctor:
Use your own words to describe how to determine the initial value from an equation.
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4.4 Initial Value.notebook
April 03, 2014
Consolidation
Determine the initial value for the following linear relation.
A) description (words)
Dennis boiled a cup of water. He then placed the cup in the freezer and recorded the temperature of the water every minute. He noticed that the temperature of the water dropped 5 0C for every minute.
C) graph
B) table of values
D) equation
How do you determine the initial value from a) Words
b) Table of values
c) Graph
d) Equation
For linear relations, when the initial value is zero, the relation is referred to as a direct variation. A direct variation is a relation in which one variable is a multiple of the other.
When the initial value is NOT zero, the relation is referred to as a partial variation. A partial variation is a relation in which one variable is a multiple of the other plus a constant amount.
Which company’s relation is direct variation? Explain.
Which company’s relation is partial variation? Explain.
Words
Equation
Table of Values
Graph
direct variation
partial variation
NO initial value/base fee
HAS an initial value/base fee
y = 55x
y = 30x + 50
(0, 0)
(0, 50)
The line passes through the origin. The line does NOT pass through (0, 0)
the origin. (0, 50)
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4.4 Initial Value.notebook
April 03, 2014
Summary­Linear Relationships
Characteristics of Linear Relationships
• The first differences in a table of values are
• The graph is
A linear relationship can be expressed using words, a table of values,
a graph, and an equation.
A) Words
A video store charges a membership fee of $10 plus $2 per video if you want to rent movies.
B) Table of Values
C) Graph
D) Equation
Let C represent the total cost in dollars.
Let n represent the number of videos.
Linear relationships have a constant rate of change and an initial value.
The constant rate of change is a measure of the line’s steepness.
The initial value is y­coordinate of the point where the line crosses the y­axis.
Questions
A) Use a red pen to indicate the initial value in each of the four representations of the linear relation.
B) Use a blue pen to indicate the rate of change in each of the four representations of the linear relation.
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