Slope-intercept form of the line through $$$\left(-1, 3\right)$$$ and $$$\left(-2, 1\right)$$$

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 $$$x_{1} = -1$$$, $$$y_{1} = 3$$$, $$$x_{2} = -2$$$, and $$$y_{2} = 1$$$.

Plug the given values into the formula for a slope: $$$m = \frac{1 - 3}{-2 - \left(-1\right)} = 2$$$.

Now, the y-intercept is $$$b = y_{1} - m x_{1}$$$ (or $$$b = y_{2} - m x_{2}$$$, the result is the same):

$$$b = 3 - \left(2\right)\cdot \left(-1\right) = 5$$$

Finally, the equation of the line can be written in the form $$$y = b + m x$$$:

$$$y = 2 x + 5$$$

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

The y-intercept is $$$\left(0, 5\right)$$$A.

The x-intercept is $$$\left(- \frac{5}{2}, 0\right) = \left(-2.5, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = 2 x + 5$$$A.