1. The problem asks for the equation of a line perpendicular to the line $y = x + 1$ and passing through the point $(-1, -4)$. 2. The given line is in slope-intercept form $y = mx + c$, where $m$ is the slope. Here, $m = 1$. 3. The slope of a line perpendicular to another is the negative reciprocal of the original slope. So, the perpendicular slope $m_\perp = -\frac{1}{1} = -1$. 4. Use the point-slope form of a line equation: $$y - y_1 = m(x - x_1)$$ where $(x_1, y_1) = (-1, -4)$ and $m = -1$. 5. Substitute values: $$y - (-4) = -1(x - (-1))$$ which simplifies to $$y + 4 = -1(x + 1)$$ 6. Distribute the slope: $$y + 4 = -x - 1$$ 7. Subtract 4 from both sides: $$y = -x - 1 - 4$$ $$y = -x - 5$$ 8. This is the equation of the line perpendicular to $y = x + 1$ passing through $(-1, -4)$ in slope-intercept form $y = mx + c$.