ALGEBRA 2 LECTURE R – 1:
Inverse, Joint, and Combined Variation
Reading Assignment: Chapter 8, Pages 480 – 484
INVERSE VARIATION
Two variable, x and y, have an inverse-variation relationship if there is a nonzero number k such that
𝒙𝒚 = 𝒌 or 𝒚 =
𝒌
𝒙
 The constant of variation is k.
EXAMPLE 1: The variable y varies inversely as x, and y = 13.5 when x = 4.5.
A. Find the constant of variation, and write an equation for the relationship.
B. Find y when x is 0.5, 1, 1.5, 2, and 2.5.
X
0.5
1
1.5
2
2.5
Y
TRY THIS PAGE 482: The variable y varies inversely as x, and y = 120 when x = 6.5.
A. Find the constant of variation, and write an equation for the relationship.
B. Find y when x is 1.5, 4.5, 8, 12.5, and 14.
X
Y
1.5
4.5
8
12.5
14
ALGEBRA 2 LECTURE R – 1:
Inverse, Joint, and Combined Variation
JOINT VARIATION
If y
= kxz, then y varies jointly as x and z, and the constant of variation is k.
EXAMPLE 2: A rectangular prism has a height of 8 in., a width of w, and a length of l.
A. Write an equation for the volume of the prism, and identify the type of variation and the
constant of variation.
B. Find the volume of the prism is the length of the base is 4 inches, and the width of the base is 2
inches.
TRY THIS PAGE 483 (Top): A rectangular prism has a height, h., a width, w, and a length of 12 in.
A. Write an equation for the volume of the prism, and identify the type of variation and the
constant of variation.
B. Find the volume of the prism is the height is 4 inches, and the width of the base is 2 inches.
EXAMPLE 3: An isosceles right triangle has a side length of x.
A. Write an equation to represent the area, A, of an isosceles right triangle. Identify the type of
variation and the constant of variation.
B. Find the area of the triangle when x is 1.5, 2.5, 3.5, and 4.5
X
A
1.5
2.5
3.5
4.5
ALGEBRA 2 LECTURE R – 1:
Inverse, Joint, and Combined Variation
TRY THIS PAGE 483 (Bottom): An circle has a radius r.
A. Write an equation to represent the area, A, of the circle. Identify the type of variation and the
constant of variation.
B. Find the area of the circle when r is 1.5, 2.5, 3.5, and 4.5
r
1.5
2.5
3.5
4.5
A
COMBINED VARIATION
When more than one type of variation occurs in the same equation, the equation represents a combined
variation.
EXAMPLE 4: The rotational speeds, sA and sB, of gear A with tA teeth and gear B with tB teeth are
related as: tAsA = tBsB. A bicycle’s pedal gear has 52 teeth and is rotating at 65 revolutions per minute.
A chain links the pedal gear to a rear-wheel gear that has 18 teeth and is attached to a 26-inch wheel.
At what speed, in revolutions per minute, is the bicycle traveling?
EQUATION:
RELATIONSHIP:
SPEED:
TRY THIS PAGE 484: A bicycle’s pedal gear has 46 teeth and is rotating at 55 revolutions per
minute. If the pedal gear is linked to a rear-wheel gear that has 24 teeth, at what speed is the bicycle
traveling?
EQUATION:
RELATIONSHIP:
SPEED:
HW R – 1 Page 486 #13 – 33 ODDS