1. **State the problem:** Find the equation of the line that passes through the point $(-3, -6)$ and is perpendicular to the line $y = 1$. 2. **Understand the given line:** The line $y = 1$ is a horizontal line where the $y$-coordinate is always 1. 3. **Find the slope of the given line:** Since $y = 1$ is horizontal, its slope $m = 0$. 4. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another with slope $m$ is the negative reciprocal, so here it is $$m_{perp} = -\frac{1}{0}$$ which is undefined. This means the perpendicular line is vertical. 5. **Equation of a vertical line:** A vertical line passing through $x = a$ has the equation $x = a$. 6. **Use the point given:** The line passes through $(-3, -6)$, so the equation is $$x = -3$$ 7. **Convert to standard form:** The standard form for a vertical line is $$x = -3$$ or equivalently $$x + 3 = 0$$. **Final answer:** $$x + 3 = 0$$