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INVERSE VARIATION by Gwen Richards Dickerson Middle School

INVERSE VARIATION by Gwen Richards Dickerson Middle School. Is this the opposite of direct variation?. Bill is happy. He is thinking about that pizza he has ordered and will be delivered soon. One whole pizza just for him!!!. How does it work?. Oh look! His friend Gina is over.

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INVERSE VARIATION by Gwen Richards Dickerson Middle School

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  1. INVERSE VARIATIONby Gwen RichardsDickerson Middle School Is this the opposite of direct variation?

  2. Bill is happy. He is thinking about that pizza he has ordered and will be delivered soon. One whole pizza just for him!!! How does it work?

  3. Oh look! His friend Gina is over. Well – sharing with one person means he will get just half of the pizza! But he likes Gina. Now what?

  4. Bill looks out the window… Robert is running to his house! Guess he heard about the pizza! Now Bill gets 1/3 of it! RATS! And…

  5. Word is out on the street…. Bill is getting pizza! Who invited Spike? What is happening to Bill’s pizza? What does that have to do with an inverse variation? Oh well…

  6. Let’s look at what happened… • There was one pizza - 1 • Bill had one pizza - 1 • Gina shows up so Bill gets ½ of the pizza • Robert runs to Bill’s house – Bill gets 1/3 of the pizza • Spike is headed to Bill’s – Bill gets ¼ of the pizza! • As each person enters, Bill gets less and less pizza.

  7. And… • An algebraic form of this would be… • Y = the pizza each one gets • X = the number of people • K = the constant (one pizza) • Y = K/X • As the number of people increased, the amount of pizza each person got decreased. • That’s easy!

  8. TOC #2 – Indirect Variation • Indirect/inverse variation is a proportion that describes the proportional relationship between 2 different values. • As one variable increases, the other variable decreases. • As one variable decreases, the other variable increases.

  9. Inverse/Indirect Variation The equation: Example:

  10. Inverse/Indirect Variation • The graph: • Is NEVER a straight line. • Will NEVER cross the origin • Will NEVER cross the x or y axes

  11. Using what we did before… • If y varies inversely as x, and y = 3 when x = 12, find x when y = 4. • First find the value of the constant (K)

  12. The review… • The formula for an inverse variation is: • An example: Distance = (rate)(time) The faster you drive (increase), the less time it takes (decrease) to travel the same distance (constant).

  13. Try this one… • If Y varies inversely as X, and y = 6 when x = 12, find x when y=9.

  14. One more example… • If y varies inversely as x, if y = 15 when x = 21, find x when y = 27.

  15. Homework…. • Now it is time to practice… • Let’s get started on our homework…

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