Algebra 1 Common Core Student Edition, Grade 8-9

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

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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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