Density is how tightly packed the matter in a substance is. Therefore, how much space it takes up (volume) will not affect this.
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When mass increases and volume stays constant, the density increases. When volume increases and mass stays constant the density decreases. When they both change, then the density will depend on the rate of change of mass and the rate of change of volume.
To change density there are three ways. You can change the shape, mass or volume of the object
It is unchanged. The density is the mass divided by the volume, and as both of these numbers are halved the density does not change.
No it will not change. Density is mass divided by volume. Since the ratio of the mass is 1/2 and the volume ratio is 1/2, there is no change. The same holds true no matter how you cut the block, as both mass and volume change proportionally the same.
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.