1. The problem is to graph the equation $$2x - 4y = 12$$. 2. First, rewrite the equation in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope and $$b$$ is the y-intercept. 3. Start with the original equation: $$2x - 4y = 12$$ 4. Isolate $$y$$ by subtracting $$2x$$ from both sides: $$-4y = -2x + 12$$ 5. Divide both sides by $$-4$$ to solve for $$y$$: $$y = \frac{\cancel{-2}x}{\cancel{-4}} + \frac{12}{-4} = \frac{1}{2}x - 3$$ 6. Now the equation is in slope-intercept form: $$y = \frac{1}{2}x - 3$$ 7. The slope $$m = \frac{1}{2}$$ means the line rises 1 unit for every 2 units it moves to the right. 8. The y-intercept $$b = -3$$ means the line crosses the y-axis at the point $$(0, -3)$$. 9. To graph: - Plot the point $$(0, -3)$$ on the y-axis. - From this point, move 2 units to the right and 1 unit up to plot a second point. - Draw a straight line through these points extending in both directions. This is the graph of the equation $$2x - 4y = 12$$.