slope = change in y values divided by change in x values.
m = (y2-y1)/ (x2-x1)
pick 2 ordered pairs from the table and use the formula above.
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if there is an = sign
For a linear I can see no advantage in the table method.
Slope is rise over run, so if you have a rise of 2 and a run of 4, then the slope is 0.5. If the table gives rises and runs, then just follow the two until they meet, that should be the slope.
There are several ways to do that. For example, you can actually graph the function. Or, you can check the ratio of the differences between the points. If this ratio (change in y, divided by change in x) is constant, the function is linear.
In general you cannot. Any set of ordered pairs can be a graph, a table, a diagram or relation. Any set of ordered pairs that is one-to-one or many-to-one can be an equation, function.