Lines that are parallel run in the same direction but are non-overlapping. In a Cartesian coordinate plane, we would identify them as two lines with the same slope but different y-intercepts.
Intersecting Lines
Lines that intersect cross each other at some point. In a Cartesian coordinate plane, the only requirement is that they have different slopes.
Coincidental Lines
Lines that coincide are one and the same. In a Cartesian coordinate plane, we would identify them as two lines with the same slope and the same y-intercept. Coincident lines have an infinite number of points of intersection.
Skew Lines
To describe skew lines, we have to introduce a third dimension z. Skew lines are neither parallel, intersecting, coincidental, nor coplanar. An example of this can be seen below.
