Answer: option (C)
Step-by-step explanation: The slope of a linear function is undetermined when the line is parallel respect to the y-axis. In the current problem there is no way to observe such geometrical issue, but if we consider how to derive the slope using the following expression; [tex]m=\frac{\Delta y}{\Delta x}= \frac{y_{2}-y_{1}}{x_2-x_{1}}[/tex].
With the previous equation, we have
[tex]a) for P_{1}(-1,1), P_{2}(1,-1) m=\frac{\Delta y}{\Delta x}= \frac{-1-1}{1-(1)}=\frac{-2}{2}=1\\[/tex], therefore the slope is defined
[tex]b) for P_{1}(-2,2), P_{2}(2,2) m=\frac{\Delta y}{\Delta x}= \frac{2-2}{2-(2)}=\frac{0}{4}=0\\[/tex], therefore the slope is defined
[tex]c) for P_{1}(-3,3), P_{2}(-3,3) m=\frac{\Delta y}{\Delta x}= \frac{3-(-3)}{-3-(-3)}=\frac{6}{0}=undetermined\\[/tex]
[tex]d) for P_{1}(-4,4), P_{2}(4,4) m=\frac{\Delta y}{\Delta x}= \frac{4-(-4)}{4-(-4)}=\frac{8}{8}=1\\[/tex]
In this case, the option (C) shows that is not possible to divide over zero. Given such issue, the slope is undetermined and therefore it is a vertical line parallel to y-axis.
