1. **State the problem:** Graph the linear equation $$2x + 4y = 8$$. 2. **Rewrite the equation in slope-intercept form:** To graph easily, solve for $$y$$. $$2x + 4y = 8$$ Subtract $$2x$$ from both sides: $$\cancel{2x} + 4y = 8 - \cancel{2x}$$ $$4y = 8 - 2x$$ Divide both sides by 4: $$\frac{4y}{\cancel{4}} = \frac{8 - 2x}{4}$$ $$y = 2 - \frac{1}{2}x$$ 3. **Interpret the slope-intercept form:** The equation is now $$y = -\frac{1}{2}x + 2$$. - The slope $$m = -\frac{1}{2}$$ means the line falls 1 unit vertically for every 2 units it moves horizontally to the right. - The y-intercept $$b = 2$$ means the line crosses the y-axis at (0, 2). 4. **Find the x-intercept:** Set $$y = 0$$ and solve for $$x$$. $$0 = -\frac{1}{2}x + 2$$ Add $$\frac{1}{2}x$$ to both sides: $$\frac{1}{2}x = 2$$ Multiply both sides by 2: $$x = 4$$ So the x-intercept is at (4, 0). 5. **Plot the points and draw the line:** - Plot (0, 2) on the y-axis. - Plot (4, 0) on the x-axis. - Draw a straight line through these points extending in both directions. This is the graph of the equation $$2x + 4y = 8$$.