Final answer:
For line k with a slope of -2p/5 to be parallel to the y-axis, the slope should be undefined. Since the given slope is not undefined, the value of p cannot be determined from the information given, suggesting a possible error in the question.
Step-by-step explanation:
The question asks about the properties of lines in the xy-plane. Specifically, it provides information that line k has a slope of -2p/5 and wants to determine the value of p for the line that is parallel to the y-axis. In coordinate geometry, a line parallel to the y-axis has an undefined slope because it rises infinitely for no horizontal movement (a vertical line). This is in contrast to a horizontal line which has a slope of 0 because it does not rise as it moves horizontally.
Given the slope of line k is -2p/5, for it to be parallel to the y-axis, the slope must be undefined. However, the slope given is a rational number, and a slope is only undefined when the denominator is zero, which does not occur in this case. Therefore, p cannot be any real number if the line is truly parallel to the y-axis. This suggests there might be an error in the given information, as no value of p will make the slope undefined.
Nevertheless, if the question implies that the slope of line k should be 0 to make it parallel to the X-axis (a common mistake), then setting the slope to 0 would give us the possible answer. For -2p/5 to be zero, p must be 0. But since the line is said to be parallel to the y-axis, the slope -2p/5 cannot simply become 0, and this contradiction points to a misinterpretation or error in the question's premise.