AA
9-4 Direct, Joint, and Inverse
Variation
Direct Variation:
* When an equation is in the form y = kx.
1. If y varies directly as x and y = -15 when
x = 5, find y when x = -3.
* k is a constant (called a constant of
variation). It is some nonzero number.
* Will form a straight line.
* If k is not given, you will be able to find it.
Joint Variation:
* When an equation is in the form y = kxz.
* k is a constant (called a constant of
variation). It is some nonzero number.
* When one quantity varies directly as the
product of two or more other quantities.
* y varies jointly as x and z.
(How you will see it written usually.
x ≠ 0, z ≠ 0, and k ≠ 0)
* If k is not given, you will be able to find it.
2. Suppose y varies jointly as x and z. Find y
when x = 10 and z = 5, if y = 12 when
z = 8 and x = 3.
Inverse Variation:
* When an equation is in the form xy = k or
k
y=
x
* k is a constant (called a constant of
variation). It is some nonzero number.
3. If a varies inversely as b and a = -6 when
b = 2, find a when b = -7.
* As one quantity increases, the other
quantity decreases. (As your speed
increases, the time of arrival will
decrease.)
* y varies inversely as x if there is some
non-zero constant k (x ≠ 0).
* If k is not given, you will be able to find it.
5.
4. The length S that a spring will stretch
varies directly with the weight F that is
attached to the spring. If a spring stretches
20 inches with 25 pounds attached, how far
will it stretch with 15 pounds attached?
The area A of a trapezoid varies jointly as its height and
the sum of its bases. If the area is 480 square meters
when the height is 20 meters and the sum of the bases
are 48 meters, what is the area of a trapezoid when its
height is 8 meters and its bases are 10 meters and 15
meters?
9 - 4 Direct, Joint, and Inverse Variation
pg. 495 - 498
#14, 16, 17, 18, 20, 21, 23, 26, 28, 31, 34,
39, 41 - 43, 56, 59, 62, 66, 67
20 problems