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Indirect Variation
What is it and how do I know
when I see it?
Definition:
k
Y varies indirectly as x means that y =
x
where k is the constant of variation.
Another way of writing this is k = xy
In other words:
* As X increases in value, Y decreases or
* As X decreases in value, Y increases.
Examples of Indirect Variation:
X
4
6
8
Note: X increases,
Y
12
8
6
4, 6, 8
And Y decreases.
12, 8, 6
What is the constant of variation of the table above?
k
Since y = x we can say
k  xy Therefore:
4•12=k or k = 48
6•8=k or k = 48
6•8=k or k =48
Note k stays constant.
y = 48/x is the
equation!
Examples of Indirect Variation:
X
30
15
5
Y
5
10
30
Note: X decreases,
30, 15, 5
And Y increases.
5, 10, 15
What is the constant of variation of the table above?
k
Since y = x we can say k  xy Therefore:
30•5=k or k = 150
15•10=k or k = 150
5•30=k or k =150
Note k stays constant.
y = 150/x is
the equation!
What is the constant of variation for
the following indirect variation?
1.
2.
3.
4.
-9
9
-1/9
1/9
X
1
3
9
18
Y
9
3
1
.5
Is this an indirect variation? If yes, give the constant
of variation (k) and the equation.
X
Y
Yes!
24
2
12
4
k = 24•2 or 48
Equation?
y = 48/x
2
24
Is this an indirect variation? If yes, give the constant
of variation (k) and the equation.
X
Y
No!
7
5
15
2
20
2.5
The y-values decrease,
but then increase!
The k values are also
different!
Which is the equation that describes
the following table of values?
1.
2.
3.
4.
y = -2/x
y = 2/x
y = -200/x
y = 200/x
X
Y
50
4
20
10
10
20
Using Indirect Variation to find unknowns (y = k/x)
Given that y varies indirectly with x, and y = 12 when
x=4, Find y when x = 12.
HOW???
2 step process
1. Find the constant variation
k = xy or k = 12•4 = 48
k=48
X
Y
4
12
12
?
2. Use y = k/x. Find the unknown (y).
y=48/12
y= 4
Therefore:
Y =4 when X=12
Using Indirect Variation to find unknowns (y = k/x)
Given that y varies indirectly with x, and y = 100 when x=25,
Find x when y = 500.
HOW???
2 step process
1. Find the constant variation.
k = yx or k = 100•25
X
Y
25
100
500
K = 2500
2. Use y = k/x. Find the unknown (x).
500 = 2500/x
x=5
Therefore:
X = 5 when Y = 500
Using Indirect Variation to solve word
problems
Problem:
A gas with volume 45
cubic inches is under a
pressure that is 75 pounds
per square inch. Find the
pressure when the volume
is 80 cubic inches.
Step Two: Find the constant
variation and equation:
k = xy or k = 45•75 = 3375
y = 3375/x
Step One: Find points in table.
X (volume)
45
80
Y (pressure)
75
?
Step Three: Use the equation
to find the unknown.
y = 3375/80
y = 42.1875
Using Indirect Variation to solve word
problems
Problem:
A gas with volume 30
cubic inches is under a
pressure that is 40
pounds per square inch.
Find the pressure when
the volume is 60 cubic
inches.
Step Two: Find the constant
variation.
k = xy or k = 30•40 = 1200
k = 1200
Step One: Find points in table.
X (volume)
Y (pressure)
30
40
60
?
Step Three: Use the equation
to find the unknown. y=k/x
y = 1200/60
y = 20
Indirect Variation and its graph
With indirect variation the equation
is y = k/x
Note: Because one variable is always doing the opposite
of the other variable, the graph will never go through….
the ORIGIN!!!!!
The graph of Indirect Variation