1. **State the problem:** Find the equation of the line passing through the points (-5, -5), (-2, -2), (3, 3), and (7, 7). 2. **Formula used:** The equation of a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$:** Use any two points, for example, (-5, -5) and (-2, -2). $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - (-5)}{-2 - (-5)} = \frac{-2 + 5}{-2 + 5} = \frac{3}{3} = 1$$ 4. **Find the y-intercept $b$:** Since the line passes through the origin (0, 0), the y-intercept is 0. 5. **Write the equation:** Substitute $m=1$ and $b=0$ into the formula: $$y = 1 \cdot x + 0$$ which simplifies to $$y = x$$ 6. **Verify with other points:** Check point (3, 3): $y = 3$ and $x = 3$, so $y = x$ holds true. **Final answer:** The equation of the line is $$y = x$$.