Linear Functions
Consider this problem:
Fran decides to track the snowfall today. There are already 2 inches on
the ground from the day before. Fran measures the snow from today’s
storm at the end of each hour. Show found that exactly 1.5 inches of snow
fell each hour. If it snowed at the rate for 5 hours, how much snow was on
the ground at the end of each hour?
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Highlight the important information. What do you know?
Highlight the question. What do you need to find out?
The table below represents the snowfall measurements. Use what you
know to complete the table.
Time (h)
Amount of Snow on the
Ground (in.)
0
1
2
3
4
5
2
Describe how you completed your table.
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Can you create an equation to represent the situation? Fill in the blanks to
create a function rule to represent this situation. Let y represent the
snowfall and x represent the number of hours:
y = _______ x + ________
In linear functions, the initial value for a linear function is the
_______________________________of a graph, or the value of y when x
Example 1: The table and graph shows how much a store earns for
selling t-shirts and hats. Find the initial value, rate of change, and
equation for each function. Compare the functions.
equals ______. The rate of change is the ratio of a function’s vertical
change (difference in y-values) to its horizontal change (difference in xvalues).
Let’s look at the graph of the function:
Example 2: The following graph compares Mr. Brown and Mrs. White’s
payments for their used cars. Explain each payment plan by analyzing the
initial value and rate of change for each function.
How is the initial value and rate of change used to create the
equation of a linear function?
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Comparing Linear Functions – Guided Practice
1.
For each function table below, identify the initial value
and rate of change. Then, determine its equation.
a.)
Initial value: ________________
Rate of Change: __________________
Equation: _________________
b.)
Initial value: ________________
Rate of Change: __________________
Equation: _________________
2. To bowl at Ten-Pin Lanes, the total cost depends on the number of
games played. The following table shows the cost for 4 games played.
What is the rate? What does it represent?
What is the initial value? What do you
think it represents?
4. For field trips, a museum charges a flat fee plus an
additional rate for each student. The following table shows that
the total cost depends on the number of students.
A.)
What is the rate of change, and what does it represent?
B.)
What is the equation that represents this situation?
What is the equation for this situation? ____________________________
-----------------------------------------------------------------------------------------3. To rent a limousine from Deluxe Limousines, a customer must pay a
set fee plus an additional amount per hour, as shown by the graph below.
Identify and interpret the initial
value and rate of change.
C.) The initial x-value for the table is 1. Explain why it is
more appropriate for the table to start at x = 1 than at x = 0.
Write an equation to represent
The situation.
___________________________
How much does it cost to rent a limo for 8 hours? ___________________