Question

Is the relationship between the variables a direct variation, an inverse variation, or neither?

Answer 1

Option B: Inverse variation $y=\frac{18}{x}$

Explanation:

Given that the set of data in the table.

Option A: Direct variation $y=3x$

For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation $k=\frac{y}{x}$

(2,9) ⇒ $k=\frac{9}{2}=4.5$

(3,6) ⇒ $k=\frac{6}{3}=2$

Since, the values of the constants are not equal.

The relationship does not represent a direct variation $y=3x$

Option A is not the correct answer.

Option B: Inverse variation $y=\frac{18}{x}$

For the relationship to be a inverse variation, then the variables must satisfy the condition for inverse variation $y=\frac{k}{x}$ ⇒ $k=yx$

(2,9) ⇒ $k=(9)(2)=18$

(3,6) ⇒ $k=(6)(3)=18$

(4,4.5) ⇒ $k=(4.5)(4)=18$

(5,3.6) ⇒ $k=(3.6)(5)=18$

Since, all the results of the constants are equal.

The relationship represents an inverse variation $y=\frac{18}{x}$

Option B is the correct answer.

Option C: Direct variation $y=1.5x$

For the relationship to be a direct variation, then the variables must satisfy the condition for direct variation $k=\frac{y}{x}$

(2,9) ⇒ $k=\frac{9}{2}=4.5$

(3,6) ⇒ $k=\frac{6}{3}=2$

Since, the values of the constants are not equal.

The relationship does not represent a direct variation $y=1.5x$

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.