Step-by-step explanation:
Given;
We are given an equation as shown below;
![2y=3x](https://img.qammunity.org/2023/formulas/mathematics/college/e6wy2r3vnzqqhbacxzjh0lj4i2rzgnq9xr.png)
Required;
We are required to determine if this is a direct variation or an inverse variation.
Step-by-step solution;
To solve for the variable y,
![2y=3x](https://img.qammunity.org/2023/formulas/mathematics/college/e6wy2r3vnzqqhbacxzjh0lj4i2rzgnq9xr.png)
![\begin{gathered} Divide\text{ }both\text{ }sides\text{ }by\text{ }2: \\ (2y)/(2)=(3x)/(2) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/d3lumr4ae73l7gu08nbdkhe8sp1hvsb2m8.png)
![y=(3)/(2)x](https://img.qammunity.org/2023/formulas/mathematics/middle-school/84xu0h83is1lio8gjmtkbdlxpzhkbmrh61.png)
ANSWER:
This is a direct variation.
Note that the constant value, 3/2 is the constant of variation.
The third option is the correct answer.