Algebra I
Name:
Block:
DV/IV
Review
Date:
Direct/Inverse Variation Review
𝒂
Direct Variation y = ax
a = constant of variation
as x↑, y↑ (assuming positive x and y)
Inverse Variation y = 𝒙 or xy = a
a = constant of variation
as x↑, y↓ (assuming positive x and y)
1) Select three of the points below that will create a relation that is a direct variation.
(1, 10) (3.5, 7) (4, 8) (8, 4) (8, 16) (10, 6)
2) Describe the graph of direct variation.
3) Which of these equations is a direct variation?
A) y  5 x  1
B) y  5 x
C) y  5
D) y  5 x  1
4) If y varies directly as x, what is the equation for the direct variation shown in the table below?
A) y  2 x  3
1
x
3
3
C) y 
x
D) y  3 x
B) y =
X
-3
-2
0
1
2
Y
-9
-6
0
3
6
5) A relation is shown in this table.
X
Y
1
10.00
4
2.50
8
1.25
20
0.50
Which statement about this relation is true?
A)
B)
C)
D)
It is a direct variation because y  2.5 x  12.5
It is an inverse variation because y  2.5 x  12.5
It is a direct variation because 10  xy
It is an inverse variation because 10 = xy
6) The graph of the equation representing a direct variation passes through point A. Plot two
additional points that lie on the graph of this equation.
7) This relation is an inverse variation.
{(1,8), (4, 2), (2, 4)}
Which equation represents this relation?
A) y  3x  5
B) y  2 x
x
8
8
D) y 
x
C) y 
8) An experiment is conducted on a container of gas that is kept at a constant temperature.




When the pressure one the gas is 30 pounds per square inch, the volume is 120 cubic inches.
When the pressure on the gas is 40 pounds per square inch, the volume is 90 cubic inches.
Let p represent the pressure on the gas.
Let v represent the volume of the gas.
Which statement is true about this relationship?
A)
B)
C)
D)
The volume of the gas varies directly with the pressure because v = 4p.
The volume of the gas varies inversely with the pressure because v = 4p.
The volume of the gas varies directly with the pressure because vp = 3,600.
The volume of the gas varies inversely with the pressure because vp = 3,600.