the density of copper is 8.92g/cm^3. If you plotted the mass of copper in grams versus the volume in cubic centimeters, what would the slope of the line be?
To determine the slope of the line when plotting the mass of copper in grams against its volume in cubic centimeters, we need to recall the formula for calculating the slope of a straight line, which is:
slope = (change in y-coordinates) / (change in x-coordinates)
In this case, the y-coordinate represents the mass of copper in grams, and the x-coordinate represents the volume in cubic centimeters.
Since density is defined as the mass per unit volume, we can rewrite the given information as follows:
density of copper = mass / volume
mass = density of copper * volume
Now, let's consider two data points from the line: (mass1, volume1) and (mass2, volume2).
The change in y-coordinates will be mass2 - mass1, and the change in x-coordinates will be volume2 - volume1.
Therefore, the slope will be:
slope = (mass2 - mass1) / (volume2 - volume1)
However, in this case, we are given the density of copper, which allows us to calculate the mass from the volume using the formula we derived earlier. So, we can rewrite the slope equation:
slope = [(density of copper * volume2) - (density of copper * volume1)] / (volume2 - volume1)
Finally, we substitute the known density of copper (8.92 g/cm^3) into the equation:
slope = [(8.92 g/cm^3 * volume2) - (8.92 g/cm^3 * volume1)] / (volume2 - volume1)
Thus, the slope of the line would be given by this equation, with the actual value requiring the specification of the specific volume points on the line.