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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 • 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 increased. • That’s easy!

  8. What is a direct variation? • A proportion that describes the relationship between 2 different values. • An equation of the form y = kx, where • K 0 • As x increases y increases or as x decreases y decreases • The graph is a straight line that always passes through the origin.

  9. Using what we did before… • Find the constant and write an equation. - plug in 12 for y and 3 for x - 12=k3 - solve the equation for k - k=4 - write the equation by replacing the constant with its’ value  y=4x

  10. Using what we did before… 2. Using that equation, find x when y = 4. - Plug the value given for y into our original equation: y=4x - 4 = 4x - Solve for x - x = 1

  11. The direct variation equation is…

  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. Am I a direct variation? 1. Does the following table represent a direct variation? • Are both x and y increasing or both decreasing? • For EVERY ordered pair, is the result of y/x the same? • If YES to both, then it is a direct variation!! 2. Does the following table represent a direct variation? • Are both x and y increasing or both decreasing? • For EVERY ordered pair, is the result of y/x the same? • If YES to both, then it is a direct variation!!

  16. What is the constant? 1. Find the constant: 2. Find the constant:

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