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Graphing and Relationships of Variables A graph is a diagram that illustrates by means of points and lines a relationship between different variables whose values are plotted on the graph. Graphical analysis also helps us determine the type of mathematical equation that relates the variables being graphed. Part 1: Graphing procedures 1. The data is most commonly plotted on Cartesian paper in which the lines are set up in a linear fashion. The horizontal line with the value of zero is called the x-axis and the vertical line with the value of zero is called the y-axis. You may be told to plot one variable versus another. If so, the variable given before the "versus" goes on the y- axis and the variable after versus goes on the x- axis. In general when plotting data, the independent variable (the one the experimenter controls) goes on the x-axis and the dependent variable goes on the y-axis. This is not a hard and fast rule, and may be changed by the instructor during some labs. 2. When plotting data, choose axis scales that are easy to plot and read. If possible, choose scales so that over half of each axis is used to plot data points. (At times, for the graphs to start at zero, this rule may need to be ignored.) Graph A illustrates an example of scales that are too small. Graph B shows the data plotted with more appropriate scales. The scales must be uniform, i.e. every small box is worth the same amount. 3. When the data points are plotted, draw a smooth best-fit line for the points. It is appropriate to ignore a data point that seems far off . Never go dot to dot as shown in Graph A. If the best fit is a straight line, always use a ruler to draw the line. If the best fit for the data is a curved line, use a French curve if you are unable to draw a smooth curve. 4. In cases where several sets of data are taken for each trial, the average value is plotted. If more than one line is plotted, be sure to label the lines or provide a key. 5. Make sure all graphs have the following: a) Each axis labeled with quantity plotted. b) The unit of the quantity plotted. c) The title of the graph on the paper (commonly listed as the y variable versus the x variable). Graphs A and B were made with the following data obtained by hanging weights on a spring and measuring how far the spring stretched. weight on spring (N) .25 .50 .75 1.00 1.25 1.50 1.75 2.00 distance spring stretched (cm) .80 2.41 2.74 3.69 5.20 6.28 6.72 8.85 *Notice how the data is completely labeled. You are expected to write down more than weight and distance when taking data. Indicate what weight and what distance. 9 0 5 10 15 20 25 1.0 0 2.0 3.0 4.0 5.0 6.0 distance w ei gh t Graph A 0 2 4 6 8 10 0.5 0 1.0 1.5 2.0 2.5 3.0 distance spring stretched (cm) weight on spring versus distance spring is stretched Graph B weight on spring (N)
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Part 2: Processing straight line graphs A graph in which the data points yield a straight line is called a linear graph. When the intercept is zero, we say that the variable on the y-axis is directly proportional to the variable on the x-axis. That phrase “directly proportional” tells you that if the variables doubles, so does the other.
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  • Spring '16
  • Tim, Sally Veight

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