1. The problem states that $y$ is directly proportional to $x$ cubed. This means we can write the relationship as: $$y = kx^3$$ where $k$ is the constant of proportionality. 2. To find $k$, we need a specific value of $y$ for a given $x$. Without that, we can only express $y$ in terms of $k$ and $x$. 3. The key rule here is that "directly proportional" means if $x$ changes, $y$ changes by the cube of $x$ times the constant $k$. 4. So the general formula for this problem is: $$y = kx^3$$ This formula shows how $y$ depends on $x$ cubed with a constant multiplier $k$. 5. If you have a specific point $(x_0, y_0)$, you can find $k$ by: $$k = \frac{y_0}{x_0^3}$$ Then substitute back to get the exact function. Final answer: $$y = kx^3$$