In rise over run, when does the run ever go left?

it can go to the left when the slope is negative.

for example, if the slope is -3/4, you can look at it two ways:
"rise/run" = (-3) / (+4) = (down 3) / (right 4)
OR
"rise/run" = (+3) / (-4) = (up 3) / (left 4)

they both give you the same line, just different directions.

No

If the x coordinate is minus it moves to the left of the origin (0, 0)