G o t It? 1. Suppose y varies inversely with x, an d y = 9 w h en x = 6. W hat is an
eq u a tio n for th e inverse variation?
Problem 2 Using Inverse Variation GRI D DED RESPON SE
Physics The weight needed to balance a lever varies inversely with the
distance from the fulcrum to the weight. How far away from the
fulcrum should the person sit to balance the lever?
160 lb
.----------------------------------------------
1000 lb
Is y o u r answer
reasonable?
The heavier object
must be closer to the
fulcrum to balance the
lever. Since the elephant
weighs more than the
person, the person
should sit more than 7 ft
from the fulcrum.
Relate The 1000-lb elep h a n t is 7 ft from th e fulcrum. The 160-lb perso n is x ft from the
fulcrum. Weight an d distance vary inversely.
Define Let w eight1 = 1000 lb. Let distance j = 7 ft. Let w eight2 = 160 lb.
Let d ista n c e 2 = x ft.
Write weight y • distancej = weight2 • distance2
1000 • 7 = 160 • x
7000 = 160x
43.75 = x
Substitute.
Simplify.
Divide each side by 160.
4 3.75
The p erso n should sit 43.75 ft from the fulcrum to balance th e lever.
G o t It? 2. A 120-lb w eight is placed on a lever, 5 ft from th e fulcrum. How far from the
fulcrum should an 80-lb w eight be p laced to balance th e lever?
Several graphs of inverse variations xy= k are
show n at th e right. Notice th a t each g raph h as two
u n co n n e cted parts. W hen k > 0, th e g raph lies in the
first a n d third quadrants. W hen k < 0, th e graph lies in
th e second a n d fourth q uadrants. Since k is a nonzero
constant, xy # 0. So n e ith e r x n o r y can equal 0.
As it moves away from th e origin, th e graph of an
inverse variation equ atio n ap p ro ach es th e x-axis an d
th e y-axis w ithout actually intersecting them.
r PowerAlgebra.com ^ Lesson 11-6 Inverse V ariation^699
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