3.4: Graphs of Linear Functions from Tables
Bonita will be celebrating her sixteenth birthday next month. Her parents would like to give her a surprise party at the local pool. To rent the pool for a private party costs $100 plus $55.00 for each hour the pool is rented. Write a linear function to represent the cost of the pool party and list five prices from which her parents can choose.
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Guidance
One way to graph a linear function is to first create a table of points that work with the function and therefore are on the graph. A linear function will always result in a graph that is a straight line.
To create a table, substitute values for into the function (you can choose values for ) and use the function to calculate the corresponding value for . Each pair of values is one point on the graph. It is easier to create the table if you first solve the equation for
You can also use a graphing calculator to create a table of values and graph of the function. This will be explored in Example B.
Example A
Complete the table of values for the linear function .
Solution:
Before completing the table of values, solve the given function in terms of ‘ ’. This step is not necessary, but it does simplify the calculations.
Example B
Use technology to create a table of values for the linear function .
Solution:
When the table is set up, you choose the beginning number as well as the pattern for the numbers in the table. In this table, the beginning value for ‘ ’ is -2 and the difference between each number is +2. The table is consecutive, even numbers. When consecutive numbers are used as the input numbers ( -values), there is a definite pattern in the output numbers ( -values). This will be expanded upon in a later lesson.
Example C
Complete the table of values for , and use those values to graph the function.
Solution:
Concept Problem Revisited
Bonita will be celebrating her sixteenth birthday next month. Her parents would like to give her a surprise party at the local pool. To rent the pool for a private party costs $100 plus $55.00 for each hour the pool is rented. Write a linear function to represent the cost of the pool party and list five prices from which her parents can choose.
The cost of renting the pool is $100. This amount is a fee that must be paid to rent the pool. In addition, Bonita’s parents will also have to pay $55.00 for each hour the pool is rented. Therefore, the linear function to represent this situation is where ‘ ’ represents the cost in dollars and ‘ ’ represents the time, in hours, that the pool is rented.
- To determine five options for her parents, replace ‘ ’ with the values 1 to 5 and calculate the cost for each of these hours.
These results can now be represented in a table of values:
The values in the table represent the coordinates of points that are located on the graph of .
Bonita’s parents can use the table of values and/or the graph to make their decision.
Vocabulary
- Linear Function
- The linear function is a relation between two variables, usually and , in which each value of the independent variable is mapped to one and only one value of the dependent variable .
Guided Practice
1. Complete the following table of values for the linear function
2. Use technology to complete a table of values for the linear function and use the coordinates to draw the graph.
3. A local telephone company charges a monthly fee of $25.00 plus $0.09 per minute for calls within the United States. If Sam talks for 200 minutes in one month, calculate the cost of his telephone bill.
Answers:
1. Solve the equation in terms of the variable ‘ ’.
Substitute the given values for ‘ ’ into the function.
2. To enter the function into the calculator, it must be in the form . Solve the function in terms of the letter ‘ ’.
The graph can also be done using technology. The table can be used to set the window.
3. Write a linear function to represent the word problem.
The cost of Sam’s telephone bill is $43.00.
Practice
Solve each of the following linear functions in terms of the variable ‘ ’.
For each of the following linear functions, create a table of values that contains four coordinates:
For each of the linear functions, complete the table of values and use the values to draw the graph.
Using technology, create a table of values for each of the following linear functions. Using technology, graph each of the linear functions.
- Mr. Red is trying to estimate the cost of renting a car to go on vacation. He has contacted a rental agency and has obtained the following information. The agency charges a daily rate of $78.00 for the vehicle plus 45 cents per mile. If Mr. Red has $350 set aside for travel, create a table of values that will give him approximate distances that he can travel with this rental car.
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Description
Learning Objectives
Here you will learn how to create a graph of a linear function by using a table.
Difficulty Level:
At GradeCategories:
Date Created:
Dec 19, 2012Last Modified:
Apr 29, 2014Vocabulary
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