1. The problem asks for the equation of a line in slope-intercept form, which is given by the formula: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 2. We are given two points on the line: $(-10, -10)$ and $(10, 10)$. To find the slope $m$, use the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substitute the points: $$m = \frac{10 - (-10)}{10 - (-10)} = \frac{10 + 10}{10 + 10} = \frac{20}{20} = 1$$ 3. The slope is $1$. Next, find the y-intercept $b$ by substituting one point and the slope into the slope-intercept form: Using point $(10, 10)$: $$10 = 1 \times 10 + b$$ Simplify: $$10 = 10 + b$$ Subtract 10 from both sides: $$10 - 10 = b$$ $$0 = b$$ 4. The y-intercept is $0$. Therefore, the equation of the line is: $$y = 1x + 0$$ or simply $$y = x$$ 5. Comparing with the options given: A) $y = 8x + 8$ B) $y = x - 8$ C) $y = 8x - 8$ D) $y = x + 8$ None exactly matches $y = x$, but the line passes through the origin, so the correct equation is $y = x$, which is not listed. However, based on the problem statement, the slope is 1 and y-intercept is 0. Final answer: $y = x$