Inverse Variation

1. The length of
time, m, it takes
Need to know: • It is an water to boil varies
unknown
k – constant of inversely as
value – a
variation constant temperature, t.
k
m
t
Formula
• Notice the location of the
k variables; As one value
y
x increases the other decreases.
• Commonly
“y vary
written
inversely as x” this way

2. The length of time, m, it takes water to boil k
varies inversely as temperature, t. m
This means the higher the temperature, the less
t
amount of time it takes for the water to boil
Need to know: • It is an
unknown
k – constant of value – a
variation constant
Formula • Notice the location of the
k variables; As one value
y increases the other
x decreases.
• Commonly
“y vary inversely
written
as x” this way

3. The length of my legs, l, varies inversely as the
steps I must take to cross the room, s.
If it takes me 62 steps and my legs are 30 in long,
find the constant of variation.
k
___ Step 1: k
___
l = s Fill in the
given values 30 = 62
Step 2: k
___
Multiply to (62)(30)=(62)
solve for k
(62)
1860 = k

4. The length of my legs, l, varies inversely as the steps I must
take to cross the room, s. If it takes me 62 steps and my
legs are 30 in long, how many steps would it take if my legs
were only 20 in long?
l= k
___ Step 1:
Fill in the base 30 = __
k
given values 62
s
k
___
Step 2:
Multiply to
(62)(30) = (62)
solve for k (62)
1860 = k
1860
____
Step 3:
Use k and the given for the 20 = 20 s = 1860
second scenario to find the s s = 93 steps
missing value

5. The length of my legs, l, varies inversely as the steps I must
take to cross the room, s. If it takes me 62 steps and my
legs are 30 in long, how long would a persons legs be if it took
them 60 steps?
l= k
___ Step 1:
Fill in the base 30 = __
k
given values 62
s
k
___
Step 2:
Multiply to
(62)(30) = (62)
solve for k (62)
1860 = k
Step 3:
1860
____ = 31 in
Use k and the given for the
second scenario to find the l=
missing value 60