1. **State the problem:** We need to sketch the graph of the linear equation $$y = -2x - 4$$ using intercepts. 2. **Recall the formula and rules:** A linear equation in slope-intercept form is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Find the y-intercept:** The y-intercept occurs when $$x=0$$. Substitute $$x=0$$ into the equation: $$y = -2(0) - 4 = -4$$ So the y-intercept is at point $$(0, -4)$$. 4. **Find the x-intercept:** The x-intercept occurs when $$y=0$$. Set $$y=0$$ and solve for $$x$$: $$0 = -2x - 4$$ $$2x = -4$$ $$x = \cancel{\frac{2x}{2}}\frac{-4}{2} = -2$$ So the x-intercept is at point $$(-2, 0)$$. 5. **Plot the intercepts:** Plot 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 $$y = -2x - 4$$. 7. **Interpret slope:** The slope $$m = -2$$ means the line goes down 2 units for every 1 unit it moves to the right, confirming the downward slope. **Final answer:** The graph is a straight line crossing the y-axis at $$(0, -4)$$ and the x-axis at $$(-2, 0)$$ with slope $$-2$$.