7th Grade Math

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Variation

PART ABCDE

Multi-Part

Lesson 3

SPI 0706.1.3

Recognize whether

information given in a table,

graph, or formula suggests a

directly proportional, linear,

inversely proportional, or

other nonlinear relationship.

Also addresses GLE 0706.1.7,

GLE 0706.3.5.

412 Linear Functions

Inverse Variation

Refer to the rectangles below.

4 units

3 units

6 units

2 units

12 units

1 unit

1. What is the constant in each rectangle?


2. What happens to the width as the length increases?


3. What happens to the length as the width increases?

The example above shows an inverse variation. In an inverse

variation, the product of x and y is a constant. We say that y is

inversely proportional to x.

As x increases, the value of y decreases, but not at a constant rate. So,

the graph of an inverse variation is not a straight line as in a direct

variation.

Main Idea

Use inverse variation

to solve problems.

Vocabulary

inverse variation

Inverse Variation

Words An inverse variation is a

relationship where the

product of x and y is a

constant k.

Model

4

2

0

6

8

3

1

5

7

9

17283546 9

y

x

Symbols xy = k or y = _kx ,

where k ≠ 0

Example xy = 3 or y = _^3 x

V

i

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