Question

analyze the graph of two liquids. which statement best describes and explains which liquid would sink to the bottom if both were placed in a container?
mass and volume of two liquids
mass lauda a (g) = 1.8x + 0.543
mass lauda b (g) = 0.709x + 0.094
liquid a would sink to the bottom, because it has a slope (and density) of 1.8 g/ml.
liquid a would sink to the bottom, because it has a slope (and density) of 0.543 g/ml.
liquid b would sink to the bottom, because it has a slope (and density) of 0.709 g/ml.
liquid b would sink to the bottom, because it has a slope (and density) of 0.094 g/ml.

Explanation:

Step1: Understand density concept

Density formula: $
ho=\frac{m}{V}$ (where $
ho$ is density, $m$ is mass, $V$ is volume). The steeper the slope of the mass - volume graph (since slope $=\frac{\Delta m}{\Delta V}=
ho$), the higher the density.

Step2: Compare slopes (densities)

Looking at the graph, Liquid B has a steeper slope. For example, if we take two points on Liquid B's line: assume at $V_1 = 10\space mL$, $m_1=7\space g$ and at $V_2 = 20\space mL$, $m_2 = 14\space g$. Slope (density) $
ho_B=\frac{14 - 7}{20 - 10}=0.7\space g/mL$. For Liquid A, assume at $V_1'= 10\space mL$, $m_1'=5.43\space g$ and at $V_2'= 20\space mL$, $m_2' = 10.86\space g$. Slope (density) $
ho_A=\frac{10.86 - 5.43}{20 - 10}=0.543\space g/mL$. A liquid with higher density sinks.

Answer:

Liquid B would sink to the bottom, because it has a slope (and density) of $0.709\space g/mL$