1. **State the problem:** We need to find which linear inequality corresponds to the graphed solution set. 2. **Analyze the graph:** The graph shows a dashed increasing line passing through approximately points (0, -1) and (5, 1). 3. **Find the equation of the boundary line:** The slope $m$ is calculated as: $$m = \frac{1 - (-1)}{5 - 0} = \frac{2}{5}$$ Using point-slope form with point (0, -1): $$y - (-1) = \frac{2}{5}(x - 0) \implies y + 1 = \frac{2}{5}x$$ Rearranged: $$y = \frac{2}{5}x - 1$$ 4. **Rewrite the boundary line in the form given in the options:** Divide both sides by 2: $$\frac{y}{2} = \frac{1}{5}x - \frac{1}{2}$$ Add $\frac{1}{2}$ to both sides: $$\frac{y}{2} + \frac{1}{2} = \frac{x}{5}$$ 5. **Determine the inequality sign:** The graph shows shading below the dashed line, so the inequality is: $$\frac{y}{2} + \frac{1}{2} < \frac{x}{5}$$ 6. **Conclusion:** The inequality that matches the graph is option B: $$\frac{y}{2} + \frac{1}{2} < \frac{x}{5}$$