11.3 Direct and Inverse Variation
Direct variation
• 2 variable quantities
that have the same
rate or ratio have
direct variation.
• Ex., if you are paid
$5 per hour, your
pay varies directly
with the # of hours
you work.
• Variables x & y are
related by the
equations
• y/x = 5 or 5x = y
Total
pay, y
10
20
30
40
Hours
worked,
x
2
4
6
8
Rate
10/2
20/4
30/6
40/8
Direct variation
• Variables x & y vary directly if, for
constant k,
y/x = k
or
kx =y
• K is called the constant of variation
• In our example, k = 5
• If x increases or decreases so does y,
and vice versa
Indirect (inverse) variation
• Variables x & y vary inversely if, for a
constant, k…
yx = k
or
y = k/x
or
x = k/y
• K is the constant of variation
• If x or y increases, the other one
decreases and vice versa.
Indirect (inverse) variation
• If the variables x & y vary inversely,
find an equation that relates x & y when
x = 3 and y = 6
• xy = k
• (3)(6) = 18
18 is our constant of variation
• 18/x = y
or
18/y = x
Indirect (inverse) variation
1. x & y vary inversely. Find an equation that
relates x & y when x = 10 and y = 3
Answer: xy= 30 or 30/x = y or 30/y =x
2.
x & y vary directly. Find an equation that
relates x & y when x = 6 and y = 24
Answer: 4 = y/x or 4x = y
Practice
The variables x and y vary directly. Given
one pair of values for x and y, find an
equation that relates the variables.
Practice
The variables x and y vary inversely. Given
one pair of values for x and y, find an
equation that relates the variables.
Practice
Assume the variables vary directly
1. If x = 14 when y = 7, find x when y = 5.
2. If x = 6 when y = 10, find x when y = 2.
3. If x = 30 when y = 8, find x when y = 4
Practice
Assume the variables vary inversely
1. If x = 2 when y = 7, find x when y = 8.
2. If x = f when y = 18, find x when y = 3.
3. If x = i when y = 5, find x when y = 10.
Practice
Circumference and Radius
The circumference of a circle varies
directly with the length of the radius.
When the circumference is 83~ in., the
radius is 4 in.
Homework
• Pg. 578 # 7-25 odds