IDENTIFYING DIRECT ANG INVERSE VARIATION FROM TABLE

Direct variation :

Two variables x and y show direct variation when

y = ax

for some nonzero constant a.

Another type of variation is called inverse variation.

Inverse variation :

Two variables x and y show inverse variation when they are related as follows:

y = a/x, a ≠ 0

The constant a is the constant of variation, and y is said to vary inversely with x.

Tell whether x and y show direct variation, inverse variation, or neither.

Problem 1 :

Solution :

Finding the product of x and y :

x = 2

y = -12

xy = -24

x = 4

y = -6

xy = -24

x = 6

y = -4

xy = -24

x = 8

y = -3

xy = -24

The product of x and y is constant.

Finding the ratio of y t ox :

x = 2

y = -12

y/x = -6

x = 4

y = -6

y/x = -3/2

x = 6

y = -4

y/x = -2/3

x = 8

y = -3

xy = -3/8

The ratio is not a constant. So, the given table represents the direct variation.

Problem 2 :

Solution :

Finding the product of x and y :

x = 1

y = 2

xy = 2

x = 2

y = 4

xy = 8

x = 3

y = 8

xy = 24

x = 4

y = 16

xy = 64

The product of x and y is not constant.

Finding the ratio of y t ox :

x = 1

y = 2

y/x = 2

x = 2

y = 4

y/x = 2

x = 3

y = 8

y/x = 8/3

x = 4

y = 16

y/x = 4

The ratio of y to x is not constant. So, the table represents the neither relationship.

Problem 3 :

Solution :

Finding the product of x and y :

x = -4

y = 20

xy = -80

x = -3

y = 15

y/x = -45

x = -2

y = 10

y/x = -20

x = -1

y = 5

y/x = -5

The product of x and y is not a constant.

Finding the ratio of y to x :

x = -4

y = 20

y/x = -5

x = -3

y = 15

y/x = -5

x = -2

y = 10

y/x = -5

x = -1

y = 5

y/x = -5

The ratio between y to x is constant. So, the table represents inverse variation.

Problem 4 :

Solution :

Finding the product of x and y :

x = 1

y = 60

xy = 60

x = 2

y = 30

xy = 60

x = 3

y = 20

xy = 60

x = 4

y = 15

xy = 60

The product of x and y is constant.

Finding the ratio between y to x :

x = 1

y = 60

y/x = 60

x = 2

y = 30

y/x = 15

x = 3

y = 20

y/x = 20/3

x = 4

y = 15

y/x = 15/4

The ratio between y to x is not constant. So, it is direct variation.

IDENTIFYING DIRECT ANG INVERSE VARIATION FROM TABLE

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