Slope-intercept form of the line through $$$\left(3, 5\right)$$$ and $$$\left(2, 6\right)$$$

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 $$$x_{1} = 3$$$, $$$y_{1} = 5$$$, $$$x_{2} = 2$$$, and $$$y_{2} = 6$$$.

Plug the given values into the formula for a slope: $$$m = \frac{6 - 5}{2 - 3} = -1$$$.

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

$$$b = 5 - \left(-1\right)\cdot \left(3\right) = 8$$$

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

$$$y = 8 - x$$$

The slope of the line is $$$m = -1$$$A.

The y-intercept is $$$\left(0, 8\right)$$$A.

The x-intercept is $$$\left(8, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = 8 - x$$$A.