CHECKING IF THE TABLE REPRESENTS DIRECT AND INVERSE VARIATION

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.

To check if the table represents direct or inverse variation, we have to consider the following.

Check whether it is direct variation :

  • Find constant of variation (a) by multiplying x and y.
  • If the constant of variation is same, then the table will represent direct variation.

Check whether it is inverse variation :

  • Find constant of variation (a) by dividing y by x
  • If the constant of variation is same, then we can say that the table represents inverse variation.

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

Problem 1 :

direct-inverse-variation-q1

Solution:

Finding the product of x and y :

xyk=xy12132xy=158418198xy=356423253xy=581929319xy=925134374xy=12716

The product of x and y is not a constant.

Finding the ratio of y to x :

xyk=yx1213213212=111819819818=112325325323=112931931929=113437437434=11

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

Problem 2 :

direct-inverse-variation-q2.png

Solution:

Finding the product of x and y :

xyk=xy1.513.5xy=20.252.522.5xy=56.25436xy=1447.567.5xy=506.251090xy=900

The product of x and y is not a constant.

Finding the ratio of y to x :

xyk=yx1.513.513.51.5=92.522.522.52.5=9436364=97.567.567.57.5=910909010=9

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

Problem 3 :

direct-inverse-variation-q3.png

Solution:

Finding the product of x and y :

xyk=xy421xy=84614xy=84810.5xy=848.410xy=84127xy=84

The product of x and y is constant.

Finding the ratio between y to x :

xyk=yx421214=5.25614146=2.33810.510.58=1.318.410108.4=1.19127712=0.58

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

Problem 4 :

direct-inverse-variation-q4.png

Solution:

Finding the product of x and y :

xyk=xy416xy=64511xy=556.210xy=6279xy=63116xy=66

The product of x and y is not constant.

Finding the ratio of y t ox :

xyk=yx416164=4511115=2.26.210106.2=1.617997=1.28116611=0.54

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

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