Name: _________________________________ Changing Slope and y-Intercept in Prac%ce Problems 11.5.1 Pat the Plumber Applied Situations
Complete this work in your notebook. Find the Cost
Pat’s Plumbing Company charges a travel fee for every house call plus an hourly rate for the time required to complete the job. The table shows the relationship between h, the number of hours of labor, and c, the total cost for Pat’s Plumbing services.
1. Use the information provided to determine the missing values in the table. Hours, h
Total Cost, c
1
$85
2
$120
3 4
$190
5 6 7
$295
8 9 10
2. Describe the process you used to determine the missing values.
3. What is the hourly rate? How do you know?
4. What is the travel fee? How do you know?
5. What equation could be used to determine the total cost, c, for any number of hours, h?
6. Use a black colored pencil to graph this equation on Pat’s Plumbing Company Graph. Label the graph with the equation.
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Supporting STAAR™ Achievement: Algebra 1
Name: _________________________________
Changing Slope and y-Intercept in Applied Situations
Pat’s Plumbing: Making Changes Attach your Making Changes Card. Use your responses to Find the Cost and Pat’s Plumbing Company Graph to complete the following questions.
Attach Card Here
Ask Mr. Valdez for this Card
1. Predict how the change in Pat’s Plumbing Company will affect the original situation in terms of— a. the table:
b. the equation:
c. the graph:
2. Using your change situation, complete the table below showing the total cost of Pat’s Plumbing services for jobs requiring various numbers of hours of labor. Work with your partner to decide which values would be most reasonable to include in the table.
Hours, h
Total Cost, c
3. Write an equation that could be used to represent the total cost, c, for any number of hours, h, for your change situation.
4. Revisit Pat’s Plumbing Company Graph. Add the graph of your change situation on the same graph as the original function. Use the color listed for your change situation to graph it. 5. Compare and contrast your change situation with the original situation in terms of— a. the tables:
b. the equations:
c. the graphs:
6. Was your prediction correct? Why or why not?
© Region 4 Education Service Center All rights reserved.
Supporting STAAR™ Achievement: Algebra 1
Name: _________________________________
Changing Slope and y-intercept Notes Page
Changing Slope and y-Intercept in Applied Situations
As each situation is discussed, complete the corresponding row of the table below.
Equation Representing the Situation Original Situation 1: (Red) Pat’s Plumbing Company decided to increase their hourly rate by 20% and to keep the travel fee the same. Situation 2: (Blue) Pat’s Plumbing Company decided to decrease their hourly rate by 20% and to keep the travel fee the same. Situation 3: (Green) Pat’s Plumbing Company decided to increase the travel fee by $20 and to keep the hourly rate the same. Situation 4: (Purple) Pat’s Plumbing Company decided to decrease the travel fee by $20 and to keep the hourly rate the same. Situation 5: (Orange) Pat’s Plumbing Company decided to increase the hourly rate by 20% and to decrease the travel fee by $20.
c
35h
Slope Compared to Original Function
y-intercept Compared to Original Function
50
Same
C = 42h +50
Steeper Less Steep Same
Why?
Same
The hourly rate Greater Than increased 20% Less Than
Why?
Same
Steeper
Greater Than
Less Steep
Less Than
Same
Why?
Same
Steeper
Greater Than
Less Steep
Less Than
Same
Why?
Same
Steeper
Greater Than
Less Steep
Less Than
Same
Why?
Same
Steeper
Greater Than
Less Steep
Less Than
Why?
The travel fee did not change Why?
Why?
Why?
Why?
1. Which values from the situation affect the slope of the graph? 2. Which values from the situation affect the y-intercept of the graph?
© Region 4 Education Service Center All rights reserved.
Supporting STAAR™ Achievement: Algebra 1