1. The problem asks us to find the slope of the line passing through the points $(1, -6)$ and $(5, -1)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. Substitute the given points into the formula: $$m = \frac{-1 - (-6)}{5 - 1}$$ 4. Simplify the numerator and denominator: $$m = \frac{-1 + 6}{5 - 1} = \frac{5}{4}$$ 5. The slope of the line is $\boxed{\frac{5}{4}}$. This means for every 4 units you move horizontally, the line rises 5 units vertically.