Mary creates a table of values for a function and plots the points. she finds that the difference in the y values is the same. what kind of function did she graph?

The concept of slope applies to linear functions.  Starting from the y-intercept, if one were to go up x units and over y units, they would land on a point of the graph.  Using this information, if the difference in y-values is the same, we can conclude that Mary is dealing with a linear function.