Slope-intercept form of the line through $$$\left(5, 80\right)$$$ and $$$\left(7, 65\right)$$$

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 $$$x_{1} = 5$$$, $$$y_{1} = 80$$$, $$$x_{2} = 7$$$, and $$$y_{2} = 65$$$.

Plug the given values into the formula for a slope: $$$m = \frac{65 - 80}{7 - 5} = - \frac{15}{2}$$$.

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

$$$b = 80 - \left(- \frac{15}{2}\right)\cdot \left(5\right) = \frac{235}{2}$$$

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

$$$y = \frac{235}{2} - \frac{15 x}{2}$$$

The slope of the line is $$$m = - \frac{15}{2} = -7.5$$$A.

The y-intercept is $$$\left(0, \frac{235}{2}\right) = \left(0, 117.5\right)$$$A.

The x-intercept is $$$\left(\frac{47}{3}, 0\right)\approx \left(15.666666666666667, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = \frac{235}{2} - \frac{15 x}{2} = 117.5 - 7.5 x$$$A.