Question 14982
The board forms a right triangle, where the board itself is the hypotenuse, and the legs will be the sides of the right triangle which are 6 and x, the unknown side on the floor between where the board reaches the floor and the wall.  


{{{x^2 + 6^2 = 10^2}}}


If you are familiar with the special right triangle whose sides are 3, 4, 5, or any multiple thereof, then you are familiar with a right triangle whose sides are double these numbers: 6, 8, 10, so the unknown side is 8 feet.  


If you are NOT familiar with these special triangles, then you solve the equation 
{{{x^2 + 6^2 = 10^2}}}
{{{x^2 + 36 = 100}}}
{{{x^2 = 64}}}
x=8 feet.


Either way, the unknown side of the right triangle is 8 feet.


Now, the slope is the rise over the run, where rise is 6 feet, and the run is 8 feet.  Therefore the slope is 
{{{ m = (rise)/(run) = 6/8 = 3/4 }}}


R^2 at SCC