Question

Use the graph attached below.

Answer 1

A. 17.6

The slope of a line is defined by the equation:

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$m=\frac{47-3}{6.3-3.8}=17.6$

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

$\frac{m}{V}$

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:

$\rho = \frac{m}{V}$

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