INVERSE VARIATION by Gwen Richards Dickerson Middle School
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Transcript of INVERSE VARIATION by Gwen Richards Dickerson Middle School
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INVERSE VARIATIONby Gwen Richards
Dickerson Middle School
Is this the opposite of direct variation?
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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!!!
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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.
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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!
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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?
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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.
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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!
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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.
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Inverse/Indirect Variation
xky
xy 3
The equation:
Example:
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Inverse/Indirect Variation
The graph: Is NEVER a straight line. Will NEVER cross the origin Will NEVER cross the x or y axes
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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)
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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).
kYx
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Try this one…
If Y varies inversely as X, and y = 6 when x = 12, find x when y=9.
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One more example…
If y varies inversely as x, if y = 15 when x = 21, find x when y = 27.
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Homework….
Now it is time to practice… Let’s get started on our homework…