Discuss how graphing data can help you understand the relationship
between two characteristics of a data set(such as weught versus volume
for a homogenous solid).

Dear gazo,

To graph a data set resulting from the measurement of two
characteristics, you would draw a pair of axes at right angles, with
the horizontal axis corresponding to one characteristic and the
vertical axis corresponding to the other. Then, for each pair of
observations, you would plot a point at the intersection of the
perpendicular lines drawn from the corresponding value on each axis.
By connecting a sequence of such data points from left to right, you
would get an idea of how the characteristic corresponding to the
vertical axis varies in relation to the characteristic corresponding
to the horizontal axis.

Consult the following sites for further information on this kind of
graphing, which is known as a two-dimensional Cartesian plot.

Los Alamos Neutron Science Center: Cartesian Plots
http://lansce.lanl.gov/lansce8/epics/opi/opintro-63.html

Integrated Publishing: Coordinated Cartesian Graphs
http://www.tpub.com/content/doe/h1014v1/css/h1014v1_188.htm

In the case of weight and volume in a homogeneous solid, the data
points are expected to fall along a straight line, since the
relationship of weight to volume is linear in a homogeneous substance.
Although such a line is straight, it is not level, but tilted at a
certain angle, since every increase in volume must yield a
proportional increase in weight. One measure of its angle is called
the slope, which is computed by dividing an increase in the vertical
direction, called the rise, with the corresponding increase in the
horizontal direction, called the run.

If the data from measuring an unknown homogeneous solid are plotted so
that mass is represented by the vertical axis and volume by the
horizontal axis, and a line which is the best fit for these data
points is drawn, then the slope of the line is the density of the
solid. This is because the rise divided by the run is the same in this
case as mass divided by volume, and that, in turn, is exactly the
definition of density.

Read more about slope on the following pages.

"Measuring Slope"
http://www.primeshop.com/slope.htm

PurpleMath: Using Slope to Graph Lines
http://www.purplemath.com/modules/slopgrph.htm

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Regards,

leapinglizard


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