1. The problem is to sketch the graph of the linear equation given as $y = -\frac{8}{3}x - 6$. 2. The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = -\frac{8}{3}$ and the y-intercept $b = -6$. 4. The y-intercept means the graph crosses the y-axis at the point $(0, -6)$. 5. The slope $-\frac{8}{3}$ means for every 3 units you move to the right along the x-axis, the graph moves down 8 units. 6. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = -\frac{8}{3}x - 6$$ $$\frac{8}{3}x = -6$$ $$x = -6 \times \frac{3}{8} = -\frac{18}{8} = -\frac{9}{4} = -2.25$$ 7. So the x-intercept is at $(-2.25, 0)$. 8. Plot the points $(0, -6)$ and $(-2.25, 0)$ and draw a straight line through them to sketch the graph. Final answer: The graph is a straight line with slope $-\frac{8}{3}$, y-intercept $-6$, and x-intercept $-2.25$.