1. **State the problem:** We need to graph the linear function $y = -x - 6$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = -1$ and $b = -6$. This means the line crosses the y-axis at $(0, -6)$ and slopes downward with a slope of $-1$. 4. **Find x-intercept:** Set $y=0$ to find the x-intercept: $$0 = -x - 6$$ $$x = -6$$ So the x-intercept is at $(-6, 0)$. 5. **Plot points:** Plot the points $(0, -6)$ and $(-6, 0)$ on the coordinate grid. 6. **Draw the line:** Connect these points with a straight line extending in both directions. This line slopes downward from left to right crossing the y-axis at $-6$ and the x-axis at $-6$. **Final answer:** The graph of $y = -x - 6$ is a straight line with slope $-1$ and y-intercept $-6$.