Final answer:
The set of points (15,15) and (15,16) represent a vertical line which is not a function because it fails the vertical line test. The equation for this vertical line is x = 15.
Step-by-step explanation:
The student is asking about the linear function that would correspond to the points (15,15) and (15,16). However, this makes an interesting case because both points have the same x-coordinate but different y-coordinates.
According to the principles of linear functions, a function can only have one output (y-value) for each input (x-value), which implies that these two points cannot both lie on the same line if it's a function.
In this case, because the x-coordinate is the same, the set of points would represent a vertical line, which is not a function because it fails the vertical line test.
The equation for a vertical line is x = a constant value, so in this case, the equation would simply be x = 15.