INVERSE VARIATION by Gwen Richards Dickerson Middle School

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Presentation transcript:

INVERSE VARIATION by Gwen Richards Dickerson Middle School Is this the opposite of direct variation?

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

Now what? 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.

And… 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!

Oh well… 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?

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.

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!

What is an inverse variation? An inverse variation is described by an equation of the form y = k/x, where K 0. WHY?

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)

The review… The formula for an inverse variation is: What if we solved for k, what would it look like?

To solve for k…

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

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

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