The problem asks whether the equation $y = \sqrt{8x}$ represents a proportional relationship.

1. Problem Description

The problem asks whether the equation $y = \sqrt{8x}$ represents a proportional relationship.

2. Solution Steps

A proportional relationship can be expressed in the form $y = kx$, where $k$ is the constant of proportionality. The given equation is $y = \sqrt{8x}$. This can be written as $y = \sqrt{8} \sqrt{x}$.

Let's analyze if the equation can be written in the form $y = kx$.

If we square both sides of the given equation, we get $y^2 = 8x$. This can be written as $x = \frac{1}{8} y^2$. Since the power of $x$ is 1 and $y$ is 2, this is not in the form $y = kx$.

Alternatively, we have $y = \sqrt{8} \sqrt{x}$. In order for $y$ to be proportional to $x$, we must have a relationship of the form $y=kx$. Here, $y$ is proportional to $\sqrt{x}$ instead of $x$. So it is not a proportional relationship.

3. Final Answer

Non-Proportional