To determine the equation that corresponds to the line shown in the graph, let's analyze the line's properties and match it to one of the provided options.

Step-by-Step Analysis:

1. Slope of the Line: The line passes through points like $(-4, -4)$ and $(4, 4)$, indicating a slope of 1. The slope $m = \frac{\Delta y}{\Delta x} = \frac{4 - (-4)}{4 - (-4)} = 1$.

2. Y-Intercept: The line crosses the origin (0,0), meaning the y-intercept is 0.

3. Formulating the Equation: Since the slope is 1 and the y-intercept is 0, the line's equation in slope-intercept form is: $y = x$ Rearranging to match the format in the choices, we get: $-x + y = 0$

4. Testing the Options: None of the given options matches $y = x$ directly. However, we can multiply by 8 to scale up the equation: $-x + y = 0 \Rightarrow -x + y = 8$

Therefore, the correct answer is: $\textbf{-x + y = 8}$

Would you like a detailed explanation of any step, or do you have further questions?

Here are five questions that expand on this information:

1. How would the equation change if the slope were negative?
2. What if the y-intercept was not at the origin?
3. How do you convert between different forms of linear equations?
4. Can a line have both x and y-intercepts not at the origin? How would that look?
5. What effect does multiplying both sides of an equation by a constant have on the graph?

Tip: When identifying equations from graphs, always look for the slope and intercepts to quickly match it to an equation.