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Technically, a non-zero y-intercept can't exist in such a graph. If you were looking at such a graph, it was probably because they cut it short, and were just showing part of it.
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.
Volume = mass / Density Mass = Volume * Density Density = Mass / Volume
density = mass / volume Solving for mass: mass = density x volume Solving for volume: volume = mass / density
Density = mass/volume Mass = (density) x (volume) Volume = mass/density