What is the slope of the line passing through the following points:  (7, 2) , (-8,-7)?

I found $m = \frac{3}{5}$
The slope $m$ represents the ratio of the change in $y$ as $x$ changes and gives you the inclination of a line; or:
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 7 - 2}{- 8 - 7} = \frac{9}{15} = \frac{3}{5}$
So, this number tells you that every time $x$ increases of one unit then $y$ increases of $\frac{3}{5}$.