1. **State the problem:** Find the slope of a line perpendicular to the line given by the equation $$y - 9 = 12(x + 2)$$. 2. **Rewrite the given line in slope-intercept form:** The equation is in point-slope form $$y - y_1 = m(x - x_1)$$ where $$m$$ is the slope. Given: $$y - 9 = 12(x + 2)$$ can be rewritten as $$y - 9 = 12x + 24$$. 3. Simplify to slope-intercept form $$y = mx + b$$: $$y = 12x + 24 + 9$$ $$y = 12x + 33$$ So, the slope $$m$$ of the given line is $$12$$. 4. **Recall the rule for perpendicular slopes:** If two lines are perpendicular, their slopes $$m_1$$ and $$m_2$$ satisfy: $$m_1 \times m_2 = -1$$ 5. **Find the slope of the perpendicular line:** Let $$m_2$$ be the slope of the perpendicular line. $$12 \times m_2 = -1$$ Divide both sides by 12: $$\cancel{12} \times m_2 = \frac{-1}{\cancel{12}}$$ So, $$m_2 = -\frac{1}{12}$$ **Final answer:** The slope of a line perpendicular to the given line is $$-\frac{1}{12}$$.