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?

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Supporting STAAR™ Achievement: Algebra 1

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