1. **State the problem:** We need to sketch the graph of the linear equation using intercepts for the equation $$y = -2x - 4$$. 2. **Recall the formula and rules:** The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Find the y-intercept:** The y-intercept occurs when $$x=0$$. $$y = -2(0) - 4 = -4$$ So the y-intercept is at the point $$(0, -4)$$. 4. **Find the x-intercept:** The x-intercept occurs when $$y=0$$. Set $$y=0$$: $$0 = -2x - 4$$ Add 4 to both sides: $$4 = -2x$$ Divide both sides by $$-2$$: $$\cancel{\frac{4}{-2}} = \cancel{\frac{-2x}{-2}}$$ $$x = -2$$ So the x-intercept is at the point $$(-2, 0)$$. 5. **Plot the intercepts:** Plot the points $$(0, -4)$$ and $$(-2, 0)$$ on the coordinate plane. 6. **Draw the line:** Connect these two points with a straight line. This line represents the graph of $$y = -2x - 4$$. **Final answer:** The graph is a straight line passing through the points $$(0, -4)$$ and $$(-2, 0)$$ with slope $$-2$$.