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Guide 1-3e. Finding the Slope of a Line

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 m)

         = 3.19  (units divide out)

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.

circumference vs diameter

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