Honors Algebra II/Trig
Name___________________________________________
December 2014
8.4 Variation
Date_______________________Mod_________________
TSWBAT solve and apply Direct, Inverse and Joint Variation
Algebra and Functions……………………………………2.8
Direct Variation - mathematical relationship between two variables that can be expressed by an equation in
which one variable is equal to a constant times the other, for some fixed nonzero real number k. The constant k
is called the constant of variation or constant of proportionality. y = kx
Examples:
1.) u is proportional to v. If u = 16 when v = 4, then write the formula for the relation between u and v. Find the
constant of variation.
2.) p varies directly as z. If p = 210 when z = 200, then write the formula for the relation between p and z. Find
the constant of variation.
3.) w is directly proportional to m. If w = 42 when m = 6, then find the value of m when w = 140
4.) A varies directly as b. If A = 3 when b = 8, then find the value of A when b = 1000
Inverse Variation - mathematical relationship between two variables which can be expressed by an equation in
k
which the product of two variables is equal to a constant. y 
x
1.) Suppose that y varies inversely as x and that y = 8 when x = 3. Find the constant of variation.
2.) Suppose that y varies inversely as x2 and that y = 10 when x = 2.5. Find the constant of variation.
3.) If y varies inversely as x, and y = 9 when x = 2, find y when x = 3.
Joint Variation - is the same as direct variation with two or more quantities. Joint variation is a variation where
a quantity varies directly as the product of two or more other quantities. y = kxz
1.) If y varies jointly as x and z, and y = 10 when x = 4 and z = 5, find the constant of variation.
2.) If y varies jointly as x and z, and y = 12 when x = 2 and z = 3, find y when x = 7 and z = 4.
3.) If y varies directly as x and inversely as z, and y = 5 when x = 2 and z = 4, find y when x = 3 and z = 6.
Applications
1.) The amount of sale taxes on a new car is direct proportional to purchase price of the car, if a $25000 car pays
$1750 in sales taxes. What is the purchase price of a new car which has a $3500 sale taxes?
2.) The cost of a House in Florida is proportional to the size of the house. A 2850-square-foot house cost $182400,
then what is the cost of a 3640-square-foot house?
3.) The number of days required to build a bridge is varies inversely to the number of workers. As the number of
workers increases, the number of days required to build would decrease. If 50 workers can build a bridge in 120
days, how long can 75 workers build a bridge?
4.) The number of hours h that it takes m men to assemble x machines varies directly as the number of machines
and inversely as the number of men. If four men can assemble 12 machines in four hours, how many men are
needed to assemble 36 machines in eight hours?
Homework: p. 469 #14, 16-24, 31, 32, 42-44