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You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
Data is neither a table nor a graph, however, data may be presented in a table or depicted by a graph.
You can definitely use a table or graph to what your findings. You can use a bar graph for this purpose for example.
a ratio table is a way of presenting a ratio on a math table... pretty self-explanatory
A stem and leaf plot is not a graph, but it is a table. You can turn it into a graph, a histogram, but it is simply a table that organizes your numbers.