1. **State the problem:** We need to find the equation of the line passing through the points (-5, -1), (0, -3), and (5, -5) in slope-intercept form $y = mx + b$. 2. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using points (-5, -1) and (0, -3): $$m = \frac{-3 - (-1)}{0 - (-5)} = \frac{-3 + 1}{0 + 5} = \frac{-2}{5} = -\frac{2}{5}$$ 3. **Check slope with another pair:** Using points (0, -3) and (5, -5): $$m = \frac{-5 - (-3)}{5 - 0} = \frac{-5 + 3}{5} = \frac{-2}{5} = -\frac{2}{5}$$ The slope is consistent. 4. **Find the y-intercept $b$:** Use the slope-intercept form $y = mx + b$ and point (0, -3): $$-3 = -\frac{2}{5} \times 0 + b \implies b = -3$$ 5. **Write the equation:** $$y = -\frac{2}{5}x - 3$$ 6. **Verify with another point:** Check point (-5, -1): $$y = -\frac{2}{5} \times (-5) - 3 = 2 - 3 = -1$$ Correct. **Final answer:** $$y = -\frac{2}{5}x - 3$$