1. The problem asks for the slope of the line passing through the points $(1, -2)$ and $(5, 6)$.\n\n2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:\n$$m = \frac{y_2 - y_1}{x_2 - x_1}$$\nThis formula calculates the "rise" over the "run" or the change in $y$ divided by the change in $x$.\n\n3. Substitute the given points into the formula:\n$$m = \frac{6 - (-2)}{5 - 1} = \frac{6 + 2}{5 - 1} = \frac{8}{4}$$\n\n4. Simplify the fraction by dividing numerator and denominator by 4:\n$$m = \frac{\cancel{8}^2}{\cancel{4}^1} = 2$$\n\n5. Therefore, the slope of the line is $2$.\n\nThe correct answer is B 2.