Question

Use the graph attached below.

A. Calculate the slope of the trend line. Use the yellow dots.

B. In this graph (mass vs volume), what does the slope represent?

Thanks!

Answer 1

A. 17.6

The slope of a line is defined by the equation:

`m=(y_2-y_1)/(x_2-x_1)`

where

`(x_1,y_1)` are the coordinates of the 1st point

`(x_2,y_2)` are the coordinates of the 2nd point

Here we are told to calculate the slope using the yellow dots. The coordinates of the yellow dots are (approximately):

`(x_1,y_1)=(3.8,3)\\(x_2,y_2)=(6.3,47)`

So, by applying the equation, the slope of the line is:

`m=(47-3)/(6.3-3.8)=17.6`

B. The density of the substance

In the graph represented, we have:

- Plotted on the x-axis: the volume (in mL) of a substance

- Plotted on the y-axis: the mass (in grams) of the substance

This is a straight line, so the slope is constant at every point: this means that the slope of the line is basically equal to the ratio

`(m)/(V)`

where

m is the mass

V is the volume

This quantity, however, is just the density. In fact, density is defined as the ratio between mass and volume of a substance:

`\rho = (m)/(V)`

And therefore, the slope is just the density (measured in g/mL).