1. The problem is to graph the linear function $y = -6 + x$. 2. This is a linear equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = 1$ and the y-intercept $b = -6$. 4. The slope $m = 1$ means the line rises 1 unit vertically for every 1 unit it moves horizontally. 5. The y-intercept $b = -6$ means the line crosses the y-axis at the point $(0, -6)$. 6. To find the x-intercept, set $y = 0$ and solve for $x$: $$0 = -6 + x$$ $$x = 6$$ So the x-intercept is at $(6, 0)$. 7. Plot the points $(0, -6)$ and $(6, 0)$ and draw a straight line through them to graph the function. Final answer: The graph is a straight line with slope 1 passing through $(0, -6)$ and $(6, 0)$.