Graph Line E1D7Cb

1. **State the problem:** We need to graph the equation $$-2y = x - 4$$ and identify the x- and y-intercepts. 2. **Rewrite the equation in slope-intercept form:** Solve for $$y$$. $$-2y = x - 4$$ Divide both sides by $$-2$$: $$y = \frac{x - 4}{-2} = \frac{\cancel{x} - 4}{\cancel{-2}} = -\frac{1}{2}x + 2$$ 3. **Identify the slope and y-intercept:** The equation is now $$y = -\frac{1}{2}x + 2$$. - Slope $$m = -\frac{1}{2}$$ (negative slope) - Y-intercept $$b = 2$$ (point $$(0,2)$$) 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 $$(4,0)$$. 5. **Summary:** - Y-intercept at $$(0,2)$$ - X-intercept at $$(4,0)$$ - The graph is a straight line with slope $$-\frac{1}{2}$$, crossing the y-axis at 2 and the x-axis at 4. 6. **Graph shape:** The line slopes downward from left to right, crossing the y-axis at 2 and x-axis at 4, positioned across the center/lower-center of the graph area as described.