Solve the equation for the y-value and choose whether it is a direct variation or inverse variation.

Question

3y=x

inverse variation

direct variation

Answer 1

To solve the equation \( 3y = x \) for \( y \), we can manipulate the equation as follows:

\[ y = \frac{x}{3} \]

This equation shows that \( y \) is directly proportional to \( x \). In other words, as \( x \) increases, \( y \) also increases.

Since \( y \) can be expressed as \( kx \) (where \( k = \frac{1}{3} \)), this is an example of direct variation.

Thus, the answer is:

• y-value: \( y = \frac{x}{3} \)
• Type: direct variation