Question

The answer i'm so confused

Answer 1

Slope:  rise over run, for any straight line.  Example:  y=mx + b

Constant of proportionality:  a constant by which you multiply your independent variable (x) to get a specific value of the dependent variable (y).  Example: y=kx.

The main difference here is that y=mx+b may or may not pass through the origin, whereas y=kx always passes through the origin.

Both k and m are "slopes," with k pertaining to direct variation y=kx, and m pertaining to slope of a line which may or may not pass through the origin.

In this limited sense, both k and x are slopes.  k could be the slope of a straight line passing thru the origin, same as m, but m could not be the constant of proportionality if the line in question does not pass through the origin.