Final answer:
To analyze the acceleration of a marble, plot data points from a table onto a graph, draw a best-fit line, and determine the acceleration from the slope of this line. Excel's regression tools can also be used for such analysis.
Step-by-step explanation:
To construct a graph to determine the acceleration of a marble, first, select a set of data points from a provided data table. Plot these points on a graph, making sure to fill in any blank columns in the table for quantities you graph that are different from the given data. Label your axes clearly and indicate an appropriate scale for each axis.
Once you have plotted the data points, draw a best-fit line or curve through them. This line should average out the discrepancies in the data and represent the most consistent trend in the measurements. After drawing the line, use it to determine the value of the marble's acceleration by analyzing the slope which, in the case of a velocity-time graph, represents the acceleration.
In cases where Excel is utilized, graph the data points and use the software's functionalities to generate the least-squares regression lines. Compare the slopes and the fit of these lines to your data to find the most accurate representation of the marble's acceleration.