We want to know if the function described in the following table is a linear function.
We can check the rate of change algebraically by noting the change in and change in between each of the data points.
|Changes between rows||Rate of change|
As we can see, the rate of change is constant. Therefore, we can conclude that the function is linear.
If the data points in the table represents a linear function the points will line up when plotted in a coordinate plane. Let's plot the data points as coordinate pairs.
If the function is linear, connecting these points will form a straight line. Otherwise, we will have shown that the function is nonlinear. Let's connect each of our points with a straight edge and observe the result.
It looks like they have not lined up. To be safe we will connect the first and the last point with a separate straight edge.
Since the last straight edge we drew does not coincide with the three other we can conclude that the function is nonlinear.