The graph below shows data on the Circumference vs. Diameter of cylinders. Using the coordinates of the
two points indicated on the graph, the slope is:
slope = (C2 - C1)/(D2 - D1)
= (0.121 m - 0.006
m)/(0.0380 m - 0.0020 m)
= (0.115 m)/(0.0360
= 3.19 (units
Note the following about this method of finding the slope:
Two widely-separated points are selected for use in calculating the
slope. The wider the separation, the better the precision of the final
result will be. With the points shown, the slope will have 3 significant
figures. If points were selected for which ΔC was less than
0.100 m or ΔD was less than 0.0100 m,
at most 2 significant figures could be achieved.
Data points are not selected as the two points for calculating
slope. That's because we want the slope of the line itself, and the
line doesn't necessarily pass through the data points.
The origin isn't selected as a point for calculating slope, because
the origin isn't a data point.
The locations of the two points are indicated with crosses. One could
use other symbols as long as the locations were clearly indicated.
The values of the coordinates are expressed to the greatest precision
with which the scales can be read. This is generally one-tenth of
the smallest division. This is why, for example, we write 0.0380 m instead of 0.038 m.
Units are always expressed with values.