# DIRECT AND INVERSE VARIATION WORD PROBLEMS

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 :

xy = 5

Solution :

xy = 5

Solving for x or y, we get

y = 5/x

So, it is inverse variation.

Problem 2 :

y = x − 4

Solution :

y = x - 4

It doesn't have relationship of y = ax or y = a/x. So, it is neither.

So, it is inverse variation.

Problem 3 :

y/2 = x

Solution :

y/2 = x

x = y/2

Multiplying by 2 on both sides.

2x = y

y = 2x

It is direct variation.

Problem 4 :

y = 2/x

Solution :

y = 2/x

It is in the form of y = a/x, here a is constant of variation.

So, it is inverse variation.

Problem 5 :

xy = 12

Solution :

xy = 12

y = 12/x

It is in the form of y = a/x, here a is constant of variation.

So, it is inverse variation.

Problem 6 :

y/x = 8

Solution :

y/x = 8

Multiplying by x on both sides.

y = 8x

It is in the form of y = ax, here a is constant of variation.

So, it is direct variation.

Problem 7 :

4x = y

Solution :

4x = y

y = 4x

It is in the form of y = ax, here a is constant of variation.

So, it is direct variation.

Problem 8 :

x + y = 4

Solution :

x + y = 4

It is not in the form of y = ax or y = a/x. So, it is neither.

Problem 9 :

8y = x

Solution :

8y = x

y = x/8

It is not in the form of y = ax or y = a/x, here a is constant of variation.

So, it is neither.

Problem 10 :

xy = 1/5

Solution :

xy = 1/5

y = 1/5x

It is not in the form of y = ax or y = a/x, here a is constant of variation.

So, it is neither.

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