Question: Which of the following graphs represents the equation $2x - 2y = 36$?
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 $-2$:
$$y = \cancel{\frac{-2x}{-2}} + \cancel{\frac{36}{-2}}$$
Simplifying the cancellations:
$$y = x - 18$$
3. **Interpret the slope-intercept form:**
The equation is $$y = x - 18$$, which means:
- The slope is $1$ (positive slope).
- The y-intercept is $-18$.
4. **Check the x-intercept:**
Set $y=0$:
$$0 = x - 18 \implies x = 18$$
So the line crosses the x-axis at $(18, 0)$.
5. **Match with the graphs:**
- Graph A: negative slope, crosses x and y near $-18$.
- Graph B: positive slope, crosses x near $-18$, y near $18$.
- Graph C: positive slope, crosses y near $-20$, x near $36$.
- Graph D: positive slope, crosses y near $-18$, x near $18$.
Since our line has positive slope, y-intercept $-18$, and x-intercept $18$, **Graph D** matches.
**Final answer:** Graph D represents the equation $2x - 2y = 36$.