1. **State the problem:** Find the point-slope form of the equation of a line passing through the point $(2,-1)$ with a negative slope, given the graph information. 2. **Recall the point-slope formula:** $$y - y_1 = m(x - x_1)$$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope. 3. **Identify the point:** The point given is $(2,-1)$. 4. **Determine the slope:** Using points $(0,1)$ and $(2,-1)$ from the graph, $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 1}{2 - 0} = \frac{-2}{2} = -1$$ 5. **Write the point-slope form with $m=-1$ and point $(2,-1)$:** $$y - (-1) = -1(x - 2) \implies y + 1 = -1(x - 2)$$ 6. **Check given options:** - Option b: $y + 1 = -2(x - 2)$ slope $-2$ - Option d: $y = -2x + 3$ slope $-2$ - Option a and c have positive slopes. 7. **Verify if slope $-2$ fits point $(2,-1)$:** - For option b: $$y + 1 = -2(x - 2) \Rightarrow y + 1 = -2(0) = 0 \Rightarrow y = -1$$ Matches point $(2,-1)$. - For option d: $$y = -2(2) + 3 = -4 + 3 = -1$$ Also matches point $(2,-1)$. 8. **Why choose option b over d?** Option b is in point-slope form as requested, while option d is slope-intercept form. The problem asks specifically for point-slope form, so option b is the correct choice. **Final answer:** $$\boxed{y + 1 = -2(x - 2)}$$