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

Respuesta :

6*2 =12

4*3 = 12

12*1 = 12

 answer is B inverse variation xy=12

Answer:

The correct option is B.

Step-by-step 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

[tex]y\propto\frac{1}{x}[/tex]

[tex]y=\frac{k}{x}[/tex]

[tex]xy=k[/tex]

Where, k is constant of proportionality.

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

[tex]2(6)=k[/tex]

[tex]12=k[/tex]

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

[tex]xy=12[/tex]

Therefore, the correct option is B.