Algebra 2 Inverse and Joint Variation
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Even More Variation
Inverse and Joint Variation

 

 Y can vary directly as X, but Y can also vary inversely as X.

 That means that when X goes up, Y goes down.
 The inverse of X is 1/X.
 We might also need the unit conversion constant k.
 That makes the basic inverse variation equation form:
 

 

 
 Another type of variation is joint variation.
 That means that Y varies "jointly" as more than one thing.
 The trick is, that these things are MULTIPLIED not added.
 So "Y varies jointly as X and Z" means:

 

 Y = kXY

 
 Don't forget the unit conversion constant "k"
 
 We can put a bunch of these together.
 We could say:
 "Y varies directly as X and inversely as Z"
 That translates to:

 

 
 The trick to these is that even though the words say things like X AND Z, 
 all the stuff on the right side gets multiplied together.
 
 So far, we have just used single letters for what Y varies to, 
 but we could use all kinds of stuff.
 
 We could say "Y varies inversely to X 2"
 That one is:

 
 You'll probably see one with all kinds of stuff thrown in,
 kind of like a fireworks grand finale:
 "Y varies directly as X 3 and the square root of Z
 and inversely as W 5 and log T"
 Would look like this:

 

 

   copyright 2005 Bruce Kirkpatrick

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