When can the slope of a graph represent density-?

Answer 1

When the vertical axis represents "number of things" and the horizontal represents "volume of the thing"---slope is change in vertical over change in horizontal, so units of the slope would be "number/volume", which is density.

Answer 2

density = mass / volume right? rearranging mass = density x volume mass = density x volume + 0 that resembles y = m x + b with mass = y, density = m, volume = x and b = 0 right? so if you plot mass on the y axis and volume on the x axis of a graph, the slope = density