1. **State the problem:** We need to find the point-slope form of the equation of a line that passes through the point $(2, -1)$ and has a negative slope, as described by the graph. 2. **Recall the point-slope form 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:** From the problem, the point is $(2, -1)$. 4. **Determine the slope:** The line slopes downward from left to right, indicating a negative slope. The line crosses the y-axis near $y=1$ and the x-axis between 3 and 4. Using the points $(0,1)$ and $(2,-1)$, calculate slope: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 1}{2 - 0} = \frac{-2}{2} = -1$$ 5. **Write the point-slope form:** Using $m = -1$ and point $(2, -1)$: $$y - (-1) = -1(x - 2)$$ which simplifies to $$y + 1 = -1(x - 2)$$ 6. **Compare with options:** Option b is $$y + 1 = -2(x - 2)$$ which has slope $-2$, not $-1$. Option d is $$y = -2x + 3$$ which is slope-intercept form with slope $-2$. Option a is $$y + 1 = 2(x + 2)$$ which has positive slope $2$. Option c is $$y = 2x + 3$$ which has positive slope $2$. 7. **Recalculate slope using points $(0,1)$ and $(2,-1)$:** $$m = \frac{-1 - 1}{2 - 0} = -1$$ Since none of the options have slope $-1$, check if slope $-2$ fits the point $(2,-1)$: Using option b: $$y + 1 = -2(x - 2)$$ Plug in $x=2$: $$y + 1 = -2(0) = 0 \Rightarrow y = -1$$ This matches the point $(2,-1)$. Check option d: $$y = -2x + 3$$ Plug in $x=2$: $$y = -4 + 3 = -1$$ Also matches. 8. **Conclusion:** The line has slope $-2$ and passes through $(2,-1)$, so the point-slope form is option b: $$y + 1 = -2(x - 2)$$ **Final answer:** b. $y + 1 = -2(x - 2)$