2. Inverse variation
With inverse variation the independent variable, x, appears in the denominator of the equation. An example is
where k is the constant of variation.
Types of inverse variation include:
Linear:
Quadratic:
Cubic:
Square root:
With all types of inverse variation as x increases, y
decreases and when x decreases, y increases.
y varies
inversely as x
y  1/x
y varies inversely as the
square of x
y  1/x2
y varies inversely as the
cube of x
y  1/x3
y varies inversely as the
square root of x
y  1/x

3. Example 1
The speed at which a web page downloads is inversely proportional to the number of people connected to the net. A page downloads at 30 kb/s when 6 people are connected.
a) What speed would it download the page if 5 people are online?
b) How many people were online if the page downloaded at 20 kb/s?
 write a proportion statement
a) s  1/p
b) s = 180/p
20 = 180/p
20p = 180
p = 180  20
p = 9 people
 form an equation,
add the constant of variation k
s = k/p
 sub in the initial values
30 = k/6
 solve for k
k = 30 × 6
= 180
 rewrite the equation
s = 180/p
 answer the question
s = 180/5
= 36 kb/s

4. Example 2
The intensity of the signal sent out by a data projector is inversely proportional to the square of the distance of the projector to the screen. At a distance of 3·2m the intensity is 450 candela (C).
a) What is the intensity of light 4m from the projector?
b) How far from the screen is the projector if the intensity is 128 C ?
 write a proportion statement
a) I  1/d2
b) I = 4608/d2
128 = 4608/d2
128d2 = 4608
d2 = 4608  128
d2 = 36
d = 6m
 form an equation,
add the constant of variation k
I = k/d2
 sub in the initial values
450 = k/3·22
 solve for k
k = 450 × 10·24
= 4608
 rewrite the equation
I = 4608/d2
 answer the question
I = 4608/42
= 288 C

5. Today’s work
Exercise 12G page 386
Q1, 2, 8, 9, 11 to 15