User's Manual

Discover Density Set 012–07192A
4
In algebra, the formula for a graph such as above is often given by:
y = m x + b,
where y is the variable on the vertical axis,
x is the variable on the horizontal axis,
b is the point on the vertical axis where the line intersects, and
m is the slope of the line.
The slope is found by marking two points on the line, and dividing the
difference in y-coordinates (called the rise) by the difference in x-coordinates
(the run).
Since all parts of a straight line have the same slope, the slope is a constant for
this experiment.
For this data, b is zero, and m is 2.0 km / 6.0 s = 0.33 km/s
Notice that dimensional units are part of the rise and of the run. The slope is
found in this case by dividing a distance by a time. You should recognize this
as the formula for speed.
The algebra equation y = m x + b may be translated into an equation
appropriate to this situation by replacing the algebra symbols with the variables
in the problem.
Thus, distance = speed * time, a very familiar equation!
The speed in this case is the speed of sound, and is in agreement with
published data, considering uncertainty.
This example is intended as a simple illustration of how numerical data from
an experiment is transformed from a table to a graph to a meaningful equation.