Option B: Inverse variation ![y=\frac{18}{x}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B18%7D%7Bx%7D)
Explanation:
Given that the set of data in the table.
<u>Option A: Direct variation </u>
<u></u>
For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation ![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
(2,9) ⇒ ![k=\frac{9}{2}=4.5](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B9%7D%7B2%7D%3D4.5)
(3,6) ⇒ ![k=\frac{6}{3}=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B6%7D%7B3%7D%3D2)
Since, the values of the constants are not equal.
The relationship does not represent a direct variation ![y=3x](https://tex.z-dn.net/?f=y%3D3x)
Option A is not the correct answer.
<u>Option B: Inverse variation </u>
<u></u>
For the relationship to be a inverse variation, then the variables must satisfy the condition for inverse variation
⇒ ![k=yx](https://tex.z-dn.net/?f=k%3Dyx)
(2,9) ⇒ ![k=(9)(2)=18](https://tex.z-dn.net/?f=k%3D%289%29%282%29%3D18)
(3,6) ⇒ ![k=(6)(3)=18](https://tex.z-dn.net/?f=k%3D%286%29%283%29%3D18)
(4,4.5) ⇒ ![k=(4.5)(4)=18](https://tex.z-dn.net/?f=k%3D%284.5%29%284%29%3D18)
(5,3.6) ⇒ ![k=(3.6)(5)=18](https://tex.z-dn.net/?f=k%3D%283.6%29%285%29%3D18)
Since, all the results of the constants are equal.
The relationship represents an inverse variation ![y=\frac{18}{x}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B18%7D%7Bx%7D)
Option B is the correct answer.
<u>Option C: Direct variation </u>
<u></u>
For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation ![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
(2,9) ⇒ ![k=\frac{9}{2}=4.5](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B9%7D%7B2%7D%3D4.5)
(3,6) ⇒ ![k=\frac{6}{3}=2](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B6%7D%7B3%7D%3D2)
Since, the values of the constants are not equal.
The relationship does not represent a direct variation ![y=1.5x](https://tex.z-dn.net/?f=y%3D1.5x)
Option C is not the correct answer.
Option D: Neither
Since, the relationship represents an inverse variation, the relationship cannot be neither.
Hence, Option D is the not the correct answer.