Math Pre Calc

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

• 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.

• 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

• Let x and y represent 2 quantities
• y=kxⁿ 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)

W=kH³ (equivalent to y=kx<sup>3)

Statistics shows that weight in lbs is directly proportional to the cube of height (feet).</sup>

When one variable increased, the other decreased.

ex: supply & demand (when price increased, demand decreases & vice versa.)

• y= k
• x

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.

• y=k
• x

• 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

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

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

when direct variation and inverse variation occur at the same time

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