Question

Does the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.

(Here's the table)

(x) 2 l 4 l 8 l 12 l
_____________
(y) 6 l 3 l 3/2 l 1

A: Direct Variation; y= 12/x

B: Inverse Variation; xy= 12

C: Direct Variation; y= 12x

D: Inverse Variation; y/x = 12

Answer 1

The correct option is B.

Explanation:

From the given table it is notices that the value of y decreases as x increases, therefore it is an inverse variation.

The inverse variation is defined as

`y\propto(1)/(x)`

`y=(k)/(x)`

`xy=k`

Where, k is constant of proportionality.

From the given table it is clear that the value of y is 6 at x=2.

`2(6)=k`

`12=k`

The value of k is 12. So, the required model is

`xy=12`

Therefore, the correct option is B.

Answer 2

6*2 =12

4*3 = 12

12*1 = 12

answer is B inverse variation xy=12