Slope of the line through $$$\left(1, -5\right)$$$ and $$$\left(4, 1\right)$$$

The slope of a line passing through two points $$$P = \left(x_{1}, y_{1}\right)$$$ and $$$Q = \left(x_{2}, y_{2}\right)$$$ is given by $$$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$$.

We have that $$$x_{1} = 1$$$, $$$y_{1} = -5$$$, $$$x_{2} = 4$$$, and $$$y_{2} = 1$$$.

Plug the given values into the formula for a slope: $$$m = \frac{1 - \left(-5\right)}{4 - 1} = 2$$$.

The slope of the line is $$$m = 2$$$A.