Graph Equation 834E2A

1. **State the problem:** We need to identify which graph corresponds to the equation $$2x - 2y = 36$$. 2. **Rewrite the equation in slope-intercept form:** $$2x - 2y = 36$$ Subtract $2x$ from both sides: $$-2y = -2x + 36$$ Divide both sides by $-2$: $$y = \cancel{-2} \frac{-2x}{\cancel{-2}} + \cancel{-2} \frac{36}{\cancel{-2}}$$ Simplify: $$y = x - 18$$ 3. **Interpret the slope-intercept form:** The line has slope $1$ and y-intercept $-18$. 4. **Find the x-intercept:** Set $y=0$: $$0 = x - 18 \implies x = 18$$ So the line crosses the x-axis at $(18,0)$ and the y-axis at $(0,-18)$. 5. **Match with the graphs:** - Graph A: y-intercept $18$, x-intercept $-18$ (does not match) - Graph B: y-intercept $-18$, x-intercept $36$ (x-intercept does not match) - Graph C: y-intercept $-18$, x-intercept $-18$ (x-intercept does not match) - Graph D: y-intercept $-18$, x-intercept $18$ (matches exactly) **Final answer:** Graph D represents the equation $2x - 2y = 36$.