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Direct variation
when one quantity is a constant multiple of another quantity, we say that the quantities are directly proportional to one another

Direct variation variables
 y=kx, where k is a nonzero constant
 y varies directly with x
 y is directly proportional to x
constant k is called the constant of variation or constant of proportionality.

Finding the Constant of Variation
 1) write direct variation model
 y=kx
 2) label the variables and constant
 (usually will be solving for k)
 example:
 x= number of kWh
 y= cost (increases with x)
 k= cost per kWh
3) Substitute variables, and SOLVE FOR K

Direct Variation with Powers
 Let x and y represent 2 quantities
 y=kx^{n} where k is a nonzero constant
 y varies directly with the nth power of x
 y is directly proportional to the nth power of x (however many times x occurs, y varies)

What is an example of Direct Variation with Powers?
W=kH^{3 }(equivalent to y=kx^{3)
Statistics shows that weight in lbs is directly proportional to the cube of height (feet). }

Inverse Variation
When one variable increased, the other decreased.
ex: supply & demand (when price increased, demand decreases & vice versa.)

Formula and quantities
where k is a nonzero constant
y varies inversely with x
y is inversely proportional to x
the constant k is called the constant of variation or constant of proportionality.

Solving inverse variation
 x= price of houses in thousands of dollars
 y=number of buyers
select any point on the curve
plug in points
solve for k (x multiplied times y)
plug back into original formula
 y= 100,000 = 50
 2000 <original question

Joint variation
one quantity is proportional to the product of two or more other quantities

Example of joint variation
I=Prt
 I = interest in dollars
 P= initial amount in dollars
 r= nterest rate (expressed in decimal form)
 t= time in years
total interest is proportional to these quantities

Combined variation
when direct variation and inverse variation occur at the same time

Example of combined variation
combined gas law in chemistry
 P=k T
 V
 P= pressure
 T= temp
 V= volume
 k= gas constant
 volume is inverse volume decreases, pressure increases
 temp is direct temp increases, pressure increases

