Select all of the equations below in which $v$ is directly proportional to $w$.
\[
v=\frac{3}{w} \quad v=w+3 \quad v=\frac{w}{3}
\]
\[
v=3 w \quad v=w^{3}
\]

Answer

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Answer

$\boxed{v = \frac{w}{3}, v = 3w}$ are the equations in which $v$ is directly proportional to $w$.

Steps

Step 1 ：Analyze each equation to determine if it can be written in the form $v = kw$, where $k$ is a constant.

Step 2 ：$v = \frac{3}{w}$ cannot be written in the form $v = kw$, so it does not represent direct proportionality.

Step 3 ：$v = w + 3$ cannot be written in the form $v = kw$, so it does not represent direct proportionality.

Step 4 ：$v = \frac{w}{3}$ can be written as $v = \frac{1}{3}w$, which is in the form $v = kw$. Therefore, it represents direct proportionality.

Step 5 ：$v = 3w$ is already in the form $v = kw$, so it represents direct proportionality.

Step 6 ：$v = w^3$ cannot be written in the form $v = kw$, so it does not represent direct proportionality.

Step 7 ：$\boxed{v = \frac{w}{3}, v = 3w}$ are the equations in which $v$ is directly proportional to $w$.