1. **State the problem:** Find the equation of the line passing through points $(-6,7)$ and $(-3,6)$. 2. **Formula used:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ and the point-slope form of a line is $$y - y_1 = m(x - x_1)$$. 3. **Calculate the slope:** $$m = \frac{6 - 7}{-3 - (-6)} = \frac{-1}{3} = -\frac{1}{3}$$ 4. **Use point-slope form with point $(-6,7)$:** $$y - 7 = -\frac{1}{3}(x + 6)$$ 5. **Simplify:** $$y - 7 = -\frac{1}{3}x - 2$$ 6. **Add 7 to both sides:** $$y = -\frac{1}{3}x - 2 + 7$$ $$y = -\frac{1}{3}x + 5$$ 7. **Check the options:** The correct equation is $y = -\frac{1}{3}x + 5$.