Algebra2/Trig
9.1: Direct and Inverse Variation
Name
Block
Date
Two variables, x and y, show __________ ________________ provided 𝒚 = 𝒌𝒙 𝑎𝑛𝑑 𝑘 ≠ 0

The nonzero constant (k) is called the __________________________________ and
is said to vary directly with x
Examples:
1.
The variables x and y vary directly, and y = 12 when x = 4
a.) Write an equation relating x and y
b.) Find y when x = 5
2.
The variables x and y vary directly, and y = 15 when x = 3
a.) Write an equation relating x and y
To do this: write the direct
variation equation, then
substitute for x and y and solve
for k. Then, write your equation.
b.) Find y when x = 9
Practice
Write an equation that relates the variables, and find y when x = 8.
3.
x = 2, y = 7
4.
x = 1, y = ½
5.
x = -3, y = 9
Tell whether the data set shows direct variation. If so, write an equation relating x and y.
6.
14-Karat Gold Chains
To do this, check whether the
Length, x (in)
16
18
20
24
30
quotient of y and x is a constant
Price, y (dollars) 288
324
360
432
540
7.
Weight, x (carats)
Price, y (dollars)
Loose Diamonds
0.5
0.7
1.0
2250 3430 6400
1.5
2.0
11,000 20,400
2 variables, x and y show __________ ______________ if they are related as follows:
𝒚=

𝒌
, 𝑘 ≠0
𝒙
The nonzero constant (k) is called the __________________________________ and
is said to vary inversely with x
Examples:
Tell whether x and y show direct variation, inverse variation, or neither.
𝑦
a.) = 𝑥
5
b.) 𝑦 = 𝑥 + 2
c.) 𝑥𝑦 = 4
Examples cont’d
1.
2 variables, x and y, vary inversely, and y = 8 when x = 3
a.) Write a equation that relates x and y
b.) Find y when x = 4
2.
2 variables, x and y, vary inversely, and y = 6 when x = 1.5
a.) Write a equation that relates x and y
b.) Find y when x = 4/3
To do this: write a general equation
for inverse variation, then substitute
for x and y and solve for k. Then,
write your equation.
Tell whether the data set shows inverse variation. If so, write an equation relating x and y.
3.
To do this, check whether the
x
10
20
30
40
50
product of y and x is a constant
y
30
15
10
7.5
6
4.
The table compares the wing flapping rate r (in beats per second) to the wing length l (in
cm) for several birds. Do these data show inverse variation? If so, find a model for the
relationship between r and l.
r (beats per sec)
l (cm)
Bird
Carrion crow
3.6
32.5
Common scoter
5.0
23.5
Great crested grebe
6.3
18.7
Curlew
4.0
29.2
Lesser black-backed gull
2.8
42.2
5.
The speed of the current in a whirlpool varies indirectly with the distance from the
whirlpool’s center. The Lofoten Maelstrom is a whirlpool located off the coast of Norway. At a
distance of 3 km ( _______ m) from the center, the speed of the current is about 0.1 meters
per second. Describe the change in the speed of the current as you move closer to the
whirlpool’s center.
(write an inverse variation model relating distance from center, d, and speed, s)
𝒔=
𝑘
𝒅
Fill in the table to see some speeds for different distances:
Distance from center (meters), d
Speed (meters per sec), s
Homework: textbook page 537 #21-38
2000
0.15
1500
500
250
50
2