Name__________________________________
Practice: Direct, Inverse and Joint Variation
SOL: A2.T10
1. Write and graph a direct variation equation that contains the point
(4,10)
.
Equation:
_____________
2. X and y vary directly. Write an equation that relates
x
and
y
, when x =

18 and y = 4.
Find y when x = 12.
3. X and y vary directly. Write an equation that relates
x
and
y
, when x =

12 and y = 84.
Find x when y =

4.
Tell whether the data in the table show direct variation. If so, write an equation relating x and y.
4.
5.
6. The time it takes a diver
to ascend safely to the surface varies directly with the depth. It takes a minimum of 0.75
minutes for a safe ascent from a depth of 45 feet. Write an equation that relates time and depth, then predict the
minimum time for a safe ascent f
rom a depth of 100 feet.
Tell whether x an y show a direct variation, inverse variation or neither.
7.
2 3
y x
8.
3
x
y
9.
1
2
x
y
10.
4 2( 2)
y x
11.
12.
13.
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Find y when x = 0.5.
14.
4,6
x y
15.
1
48,
12
x y
16.
2.4,3.6
x y
The
variable z varies
jointly
with x and y
. Use the given values to write an equation relating x, y and z
. Find z when
x = 4 and y=7.
17.
3.5,30
x y z
18.
1
6,,24
2
x y z
19.
3
,18,9
2
x y z
20. Boyle’s Law states that for a constant temperature, the pressure of p of a gas varies inversely with its volume. A
sample of oxygen gas has a volume of 50.25 cubic milliliters at a pressure of 20.6 atmospheres.
a.
Find the constant of varia
tion.
b.
Write an equation that relates p and V.
c.
Find the volume of the oxygen gas if the pressure changes
to 15.2 atmospheres.
Write an equation for the given relationship. (question s 21
–
23)
21. x varies directly with y and inversely with z
22. y varies jointly with x and the square of z.
23. w varies inversely with y and jointly with x and z.
Write a function for the given statement. Use k as the constant of variation.
(questions 24

29)
24. h varies directly as W, and inversely as
the square of r.
25. L varies jointly as A and H, and inversely as T.
26. The mass
M
of a concrete block varies jointly as the length
l
, width
w
and thickness
t
of the block.
27. The
collision impact
I
of an automobile varies jointly as the mass
m
and the square of the speed
v
.
28. The intensity of a sound
S
varies directly as the amplitude
A
of a sound source, and inversely as the square of
the distance
d
from the source.
29. For a
horizontal beam supported at both ends, the maximum safe load
L
, varies directly as the width
w
and the
square of the thickness
t
, and inversely as the distance d between supports.
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