1. **State the problem:** We need to identify the linear inequality represented by a graph with a solid line of slope $\frac{1}{3}$ and y-intercept $-1$, with the region shaded below the line. 2. **Recall the general form of a linear inequality:** $$y \leq mx + b \quad \text{or} \quad y \geq mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Analyze the graph details:** - The line is solid, which means the inequality includes equality ($\leq$ or $\geq$). - The slope is approximately $\frac{1}{3}$. - The y-intercept is $-1$. - The shaded region is below the line. 4. **Determine the inequality:** - Since the shaded region is below the line, the inequality is $y \leq \frac{1}{3}x - 1$. 5. **Final answer:** $$\boxed{y \leq \frac{1}{3}x - 1}$$