In the context of a graph plotting mass versus volume, the slope represents density.
Understanding the Relationship
When plotting mass on the y-axis and volume on the x-axis, the slope of the resulting line is calculated as:
Slope = (Change in Mass) / (Change in Volume) = Δm / Δv
Since density (ρ) is defined as mass (m) per unit volume (v), or ρ = m/v, the slope of the mass vs. volume graph directly corresponds to the density of the substance.
Interpreting the Slope
A steeper slope on a mass vs. volume graph indicates a higher density. This means that for a given change in volume, the corresponding change in mass is greater, implying that the substance is more dense. Conversely, a shallower slope indicates a lower density.
Example
Imagine two substances, A and B, are plotted on a mass vs. volume graph. If the line representing substance A has a steeper slope than the line representing substance B, then substance A is denser than substance B. Glancing at such a graph can quickly provide a visual comparison of densities.
