Graphing and slope

Question

A student incorrectly graphs the data and plots the volume on the y-axis and the mass on the x-axis. How will this affect the units for the slope of the line? What will the student need to do mathematically to correct the mistake and change the slope into the desired slope?

Answer 1

First question:

 

If you plot volume V on the y-axis and mass m on the x-axis, the slope will be ΔV/Δm.  The line should go through the origin, so the slope is just V/m.  This is the quantity known as "specific volume," which is the reciprocal of density.

 

Second question:

 

I assume you really want density ρ.

 

ρ = m/V

 

Then you should plot mass on the y-axis and volume on the x-axis, and the slope of a line going through the origin will be the density.