Question: Write the equation of this line in slope-intercept form. Line graph with a green line decreasing from left to right, crossing the y-axis at $(0, -6)$ and passing through points such as $(-4, -4)$ and $(4, -8)$; position_hint: center. Write your answer using integers, proper fractions, and improper fractions in simplest form.

1. **State the problem:** We need to find the equation of the line in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 2. **Identify given points:** The line crosses the y-axis at $(0, -6)$, so $b = -6$. The line passes through points $(-4, -4)$ and $(4, -8)$. 3. **Calculate the slope $m$:** $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - (-4)}{4 - (-4)} = \frac{-8 + 4}{4 + 4} = \frac{-4}{8} = -\frac{1}{2}$$ 4. **Write the equation:** Using $m = -\frac{1}{2}$ and $b = -6$, the slope-intercept form is: $$y = -\frac{1}{2}x - 6$$ 5. **Final answer:** $$\boxed{y = -\frac{1}{2}x - 6}$$