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 from a depth of 100 feet.
Tell whether x an y show a direct variation, inverse variation or neither.
7. y  2 x  3
11.
8. y 
x
3
9.
12.
2x 
1
y
10. y  4  2( x  2)
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. x  4, y  6
15. x  48, y 
1
12
16.
x  2.4, y  3.6
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. x  3. y  5, z  30
18. x  6, y 
1
, z  24
2
19. x 
3
, y  18, z  9
2
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 variation.
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.