Option B: Inverse variation [tex]y=\frac{18}{x}[/tex]
Explanation:
Given that the set of data in the table.
Option A: Direct variation [tex]y=3x[/tex]
For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation [tex]k=\frac{y}{x}[/tex]
(2,9) ⇒ [tex]k=\frac{9}{2}=4.5[/tex]
(3,6) ⇒ [tex]k=\frac{6}{3}=2[/tex]
Since, the values of the constants are not equal.
The relationship does not represent a direct variation [tex]y=3x[/tex]
Option A is not the correct answer.
Option B: Inverse variation [tex]y=\frac{18}{x}[/tex]
For the relationship to be a inverse variation, then the variables must satisfy the condition for inverse variation [tex]y=\frac{k}{x}[/tex] ⇒ [tex]k=yx[/tex]
(2,9) ⇒ [tex]k=(9)(2)=18[/tex]
(3,6) ⇒ [tex]k=(6)(3)=18[/tex]
(4,4.5) ⇒ [tex]k=(4.5)(4)=18[/tex]
(5,3.6) ⇒ [tex]k=(3.6)(5)=18[/tex]
Since, all the results of the constants are equal.
The relationship represents an inverse variation [tex]y=\frac{18}{x}[/tex]
Option B is the correct answer.
Option C: Direct variation [tex]y=1.5x[/tex]
For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation [tex]k=\frac{y}{x}[/tex]
(2,9) ⇒ [tex]k=\frac{9}{2}=4.5[/tex]
(3,6) ⇒ [tex]k=\frac{6}{3}=2[/tex]
Since, the values of the constants are not equal.
The relationship does not represent a direct variation [tex]y=1.5x[/tex]
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.
