Question

what is the slope of the hypotenuse of a 3 4 5 right triangle where 3 is horizontal side 4 is vertical side and 5 is the other side

Answer 1

If the vertical (opposite) side is 4 and the horiz. (adjacent) side is 3, then the slope of the acute angle near the horiz. side is just (4/3).

You might benefit from sketching this situation.
What if the vert. side were 3 and the horiz. side were 4? What would the slope of the hypotenuse be?

Answer 2

Slope is rise over run.
Vertical change/horizontal change
4/3 is the slope