The correct answers are options:
a. They could be parallel to each other.
c. They could be perpendicular to each other
e. They could be the same line.
Explanation:
Two lines are parallel if they do no intersect each other any point. Such lines have same slopes and the cross the y axis at different points.
Two lines can intersect either at one point or they intersect at infinite number of points. Second case occurs when both equations represent the same line so we say that the two equations have infinite number of solutions as each point will satisfy both the equations.
Two line can be perpendicular if they are at right angle to each other. This means a right angle is formed at their point of intersection. The slope of such lines is negative reciprocal of each other.
Skew lines can occur only in 3D. Two lines are skew lines if they are neither parallel nor they intersect each other at any point. Such condition can not be achieved when two linear equations are graphed on the coordinate axis.
Two equations can represent the same line when one equation is obtained by multiplying the second equation by a constant number. In this case the two equations have infinite number of solutions.