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How does it work?

DIRECT VARIATION by Gwen Richards – Dickerson Middle School modified by M. Colclasure – Pine Mountain Middle School. Bill is happy. He is thinking about that bag of candy that his mom just bought! One entire bag of candy just for him!!! That’s 25 pieces of candy all to himself!!!.

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How does it work?

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  1. DIRECT VARIATIONby Gwen Richards – Dickerson Middle School modified by M. Colclasure – Pine Mountain Middle School

  2. Bill is happy. He is thinking about that bag of candy that his mom just bought! One entire bag of candy just for him!!! That’s 25 pieces of candy all to himself!!! How does it work?

  3. Oh look! His friend Gina is over. She even brought a bag of candy with her!! Her bag has 25 pieces too!! Now, two people and 50 pieces of candy! It’s cool - Bill likes Gina. Now what?

  4. Bill looks out the window… Robert is running to his house! What’s that he’s holding? He has a bag of candy too! His bag also has 25 pieces! Now there are 3 people to share 75 pieces of candy! OH MY!! And…

  5. Word is out on the street…. Bill is having a party?! Who invited Spike? It’s okay – Spike is bringing a bag of candy to share with the group. Another 25 pieces to share! What does that have to do with a direct variation? Oh well…

  6. Let’s look at what happened… • Bill had one bag of candy - 25 pieces • Gina arrives with a bag of candy – 50 pieces • Robert runs to Bill’s house with a bag of candy – 75 pieces • Spike is headed to Bill’s with a bag of candy – 100 pieces • As each person enters, the number of pieces of candy increases

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

  8. What is a direct variation? • A direct variation is described by an equation of the form y = kx, where • K 0 • As x increases y increases. • The graph is a straight line that always passes through the origin.

  9. Using what we did before… • If y varies directly as x, and y = 12 when x = 3, find x when y = 4. • First find the value of the constant (K) • Use the formula y=kx • Plug in 12 for y and 3 for x and solve for k • 12=k3 (divide both sides by 3) • k=4 • NOW use K and the new y to find x. • 4=4x (divide both sides by 4) x=1

  10. The review… • The formula for a direct variation is: • What if we solved for k, what would it look like?

  11. To solve for k…

  12. Try this one… • If Y varies directly as X, and y = 12 when x = 6, find x when y=10.

  13. One more example… • If y varies directly as x, if y = 15 when x = 5, find x when y = 27.

  14. One more example… Problem:The cost of operating a TV varies directly as the number of hours it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 hours. • y = cost; x = number of hours • y = kx • 14 = k(30) • 14/30 = k, or k = 7/15 • Equation: • y = 7/15x

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

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