1. **State the problem:** Find the equation of the line parallel to $y = -6x + 3$ that passes through the point $(-2, 16)$. 2. **Recall the rule for parallel lines:** Parallel lines have the same slope. The slope of the given line is $m = -6$. 3. **Use the point-slope form of a line:** The formula is $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1)$ is a point on the line and $m$ is the slope. 4. **Substitute the known values:** $$y - 16 = -6(x - (-2)) = -6(x + 2)$$ 5. **Simplify the right side:** $$y - 16 = -6x - 12$$ 6. **Isolate $y$ to get slope-intercept form:** $$y = -6x - 12 + 16$$ 7. **Simplify the constants:** $$y = -6x + 4$$ **Final answer:** The equation of the line parallel to $y = -6x + 3$ passing through $(-2,16)$ is $$\boxed{y = -6x + 4}$$