A linear function is a function whose graph is a straight line.
It is given that Mary plotted a graph and she found out that the difference in the y values is the same. So such a thing could happen when a function is a linear function.
since, a linear equation is given as:
where a and b are real numbers.
so for distinct values of x say we get the y-values as
now,
so for equally spaced we get the difference in y-value to be equal.
Since the difference between each of the y values, which are the outputs, are the same, it must mean that Mary would've gotten a straight line if she graphed this function. Thus, it is a linear function.