Final answer:
Two lines in a two-dimensional coordinate system that have the same slope but different y-intercepts are parallel and do not intersect. The concept of skew lines is applicable in three-dimensional geometry, where lines do not intersect and are not parallel nor in the same plane.
Step-by-step explanation:
The issue presented is about determining the relationship between two lines in a coordinate system. Specifically, the question asks whether the lines intersect, are skew, or are parallel. When lines are skew, they are not in the same plane and do not intersect. The concept of skew lines is relevant when dealing with three-dimensional geometry rather than two-dimensional plane geometry.
To find if lines intersect, we generally look for a common point of intersection by setting equations of lines equal to each other and solving for the variables. In a two-dimensional space, if lines have the same slope but different y-intercepts, then they are parallel and will never intersect. If the lines have different slopes, they will intersect at one point. But in three-dimensional space, lines may also be skew if they are not parallel and do not intersect, which means they are non-coplanar.
From the provided information, it is implied that, graphically, a line that shifts up or down, staying parallel to the original, would have a different intercept. Thus, if two lines have the same slope but different y-intercepts (as described in the hypothetical scenario given), they will indeed be parallel and not intersect.