Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse variation?

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Course 2

Identifying IV

QUESTIONWhat are the three

ways to show inverse variation?

3 ways to show inverse variations:

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Course 2

Identifying IV

* by a table

* by an equation

* by a graph

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Course 2

Identifying IV

QUESTIONHow can a table show

inverse variation?

Table

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Identifying IV

- either x increases and y decreases, or x decreases and y increases (vary inversely)

- the product of each x and corresponding y is the same

x 30 15 5

y 1 2 6

Example of Indirect Variation:

1. As x increases (3, 12, 48), y decreases 8, 2, 1/3).

2. What is the constant of variation of the table above?

3 • 8 = k or k = 24

12 • 2 = k or k = 24

48 • 1/3 = k or k =24 Note k stays constant.

x y

3 8

48 1/3

12 2

k xy

Course 2

Identifying IV

Do these tables show IV?

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Course 2

Identifying IV

x 1 ½ ¼

y 4 8 16

x -2 0 2

y 1 0 -1

x 4.5 3 0.5

y 2 3 18

x -24 -12 -8

y -½ -1 -1 ½

YES

NOYES

YES

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Course 2

Identifying IV

QUESTIONHow can an equation

show inverse variation?

Equation

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Identifying IV

- written in the form: y = k/x

- other possible form: xy = k

- k = 0

Example: y = 4/x

Do these equations show IV?

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Identifying IV

y = 6x

2y = x y/8 = 1/x

y = 3.4/xNO

NO

YES

YES

xy = -12YES y = -4/x + 2 NO

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Identifying IV

QUESTIONHow can a graph show

inverse variation?

GraphInsert Lesson Title Here

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Identifying IV

- curved line formed by connected points will NOT go through the origin

- approaches the axes but never crosses them

Do these graphs show IV?

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Identifying IV

NO YES

NO YES

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Identifying IV

QUESTIONWhat is the proportion for indirect or inverse

variation?

Proportion:

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Identifying IV

1 2

2 1

x y

x y

1. Arrange one pair as the numerator of one ratio and the denominator of the other. 2. Arrange the other pair in the same manner.

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Identifying IV

VOCABULARY

KK II MMinverse

variation- one variable increases, other decreases- product of variables x and y is constant

y = k/x

Is this an inverse variation?

Course 2

Identifying IV

12 3 4 ( 3)y

x

3x

y

2y

x

4y

x

1

8

y

x

5y x

12xy

1 3y x

2

24y

x