1. **State the problem:** Find the volume generated when the line $y=3x$ is revolved about the x-axis from $x=0$ to $x=2$. 2. **Formula used:** The volume $V$ of a solid of revolution about the x-axis is given by the disk method formula: $$V=\pi \int_a^b [f(x)]^2 \, dx$$ where $f(x)$ is the function being revolved, and $[a,b]$ is the interval. 3. **Apply the formula:** Here, $f(x)=3x$, $a=0$, and $b=2$. So, $$V=\pi \int_0^2 (3x)^2 \, dx = \pi \int_0^2 9x^2 \, dx$$ 4. **Integrate:** $$\int_0^2 9x^2 \, dx = 9 \int_0^2 x^2 \, dx = 9 \left[ \frac{x^3}{3} \right]_0^2 = 9 \left( \frac{2^3}{3} - 0 \right) = 9 \times \frac{8}{3} = 24$$ 5. **Calculate volume:** $$V = \pi \times 24 = 24\pi$$ **Final answer:** The volume generated is $24\pi$ cubic units.