Using your knowledge of direct and inverse variations, solve each problem shown below. Follow the instructions for each portion, answer all of the questions, and make sure to show all of your work.

This activity is available below or in a printable document.

For Problem 1: Answer each question

1. If you are given a table of values, how can you determine if a direct variation exists?

For Problems 2-5: Determine if y varies directly with x. Give the constant of variation, when appropriate.

2. 
   

   x	y
   −0.5	−40
   2.5	8
   4	5

   
   
   1. Does y vary directly with x?
   2. What is the constant of variation?
      
      
3. 
   

   x	y
   4	−3
   8	−6
   12	−9

   
   
   1. Does y vary directly with x?
   2. What is the constant of variation?
      
      
4. {(3, 21), (4.5, 31.5), (5.5, 38.5)}
   
   
   1. Does y vary directly with x?
   2. What is the constant of variation?
      
      
5. {(6, 30), (7, 35), (8, 96)}
   
   
1. Does y vary directly with x?
2. What is the constant of variation?

For Problem 6: Read the scenario and answer the question.

6. Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he prepared 20 cupcakes in 30 minutes.
   
   
   1. Does the scenario represent a direct variation?
   2. If yes, explain the meaning of the constant of proportionality in the scenario.

For Problem 7: Answer the question.

7. If you are given a set of ordered pairs, how can you determine if an inverse variation exists?

For Problem 8-11: Determine if y varies inversely with x. Give the constant of variation when appropriate.

8. {(−3, −6), (2, 9), (4.5, 4)}
   
   
1. Does y vary inversely with x?
2. What is the constant of variation?
   
   
9. {(5, 4), (10, 8), (15, 12)}
   
   
1. Does y vary inversely with x?
2. What is the constant of variation?
   
   
10. 
    

    x	y
    2	25
    2.5	16
    5	10

    
    
    1. Does y vary inversely with x?
    2. What is the constant of variation?
    
    
11. 
    

    x	y
    3	−3
    9	−1
    12	−0.75

    
    
    1. Does y vary inversely with x?
    2. What is the constant of variation?

For Problem 12: Read the scenario and answer the question.

12. Scenario: Shawn hired contractors to install new carpet in two rooms in his home. The rooms are equal in size. Three contractors installed carpet in one room in hours. Four contractors installed carpet in the additional room in hours.
    
    
    1. Does the scenario represent an inverse variation? Explain your reasoning.

Once you have completed this assignment, please submit your work to the dropbox.