Slope-intercept form of the line through $$$\left(-5, 10\right)$$$ and $$$\left(10, 4\right)$$$

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 $$$x_{1} = -5$$$, $$$y_{1} = 10$$$, $$$x_{2} = 10$$$, and $$$y_{2} = 4$$$.

Plug the given values into the formula for a slope: $$$m = \frac{4 - 10}{10 - \left(-5\right)} = - \frac{2}{5}$$$.

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

$$$b = 10 - \left(- \frac{2}{5}\right)\cdot \left(-5\right) = 8$$$

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

$$$y = 8 - \frac{2 x}{5}$$$

The slope of the line is $$$m = - \frac{2}{5} = -0.4$$$A.

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

The x-intercept is $$$\left(20, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = 8 - \frac{2 x}{5} = 8 - 0.4 x$$$A.