1. The problem asks to find the equation of the line passing through the points (-7, 3) and (6, -6). 2. The formula for the slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the points into the slope formula: $$m = \frac{-6 - 3}{6 - (-7)} = \frac{-9}{6 + 7} = \frac{-9}{13}$$ 4. The slope-intercept form of a line is: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 5. Use one of the points to solve for $b$. Using point (-7, 3): $$3 = \left(-\frac{9}{13}\right)(-7) + b$$ $$3 = \frac{63}{13} + b$$ 6. Solve for $b$: $$b = 3 - \frac{63}{13} = \frac{39}{13} - \frac{63}{13} = -\frac{24}{13}$$ 7. Write the final equation of the line: $$y = -\frac{9}{13}x - \frac{24}{13}$$