Direct Variation
Wednesday, September 05, 2007
8:55 PM
Direct Variation: If a situation is described by an equation in the form y = kx
where k is a nonzero constant, we say that y varies directly as x or y is
directly proportional to x. The number k is called the constant of
variation or the constant of proportionality.
Example: Sales Tax varies directly as the sale price of an item.
The larger the sale, the more tax to be paid.
The smaller the sale, the less tax to be paid.
Other ways to say direct variation:
y varies directly as x.
y varies with x.
y is directly proportional to x.
y is proportional to x.
1310 3.3 Page 1
Inverse and Joint Variation
Saturday, February 09, 2008
9:26 PM
Inverse Variation: If a situation is described by an equation in the form
y = k/x where k is a nonzero constant, we say that y varies inversely as
x or y is inversely proportional to x. The number k is called the
constant of variation or the constant of proportionality.
Example: In the formula, T = D/R, time varies inversely as the rate, given
that D is a constant.
The faster you go, less time it takes to get there.
The slower you go, the more time it takes to get there.
Joint Variation: If a situation is described by an equation in the form y =
kxy where k is a nonzero constant, we say that y varies jointly as x and
y. The number k is called the constant of variation or the constant of
proportionality.
Example: In the formula, I = PRT (Simple Interest
Formula), the simple interest, I, varies jointly as
the simple interest rate, R, and time, T, given that
the principal, P, is a constant.
1310 3.3 Page 2
Saturday, February 09, 2008
9:55 PM
Example 1, 2 & 3
1. P varies directly as t. If t = 6, then P = 120. Find the constant
of proportionality and write the formula to express this
statement.
2. y varies inversely as the square of x. If x = 5, then
y = –3. Find the constant of proportionality and write the
formula to express this statement.
3. C varies directly with x and inversely with the square root of w. If x
= 4 and w = 36, then C = 10. Find the constant of proportionality and
write the formula to express this statement.
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1310 3.3 Page 4
Saturday, February 09, 2008
10:05 PM
Example 4 and 5
4. T varies jointly with x and then inversely with the cube of z. If x = –2
and z = 3, then
T = 6. Find the constant of proportionality and write the
formula to express this statement.
5. The cost of printing a magazine is jointly proportional
to the number of pages in the magazine and the number
of magazines printed. Find the expression to express
this statement.
Find the constant of proportionality if the printing cost is $60,000 for
the 4,000 copies of a 120 page magazine.
How much would the printing cost be for 5,000 copies of
a 92 page magazine?
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1310 3.3 Page 6
Example 6 & 7
Saturday, February 09, 2008
10:21 PM
6. The distance that an object falls varies directly as the square of the
time it has been falling. An object falls 16 feet in 1 second. How far
will it fall in 3 seconds? How long will it take an object to fall 64 feet?
7. The time required to assemble computers varies
directly as the number of computers assembled and
inversely as the number of workers. If 30 computers
can be assembled by 6 workers in 10 hours, how long
would it take 5 workers to assemble 40 computers.
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1310 3.3 Page 7