parallel lines

Parallel lines run in the same direction and stay a constant distance apart forever, like the two rails of a train track. They head the same way and never cross.

On the coordinate plane, two distinct non-vertical lines are parallel exactly when they have the same slope but different y-intercepts. Same slope means same steepness and direction; different intercepts means they are not the same line. Two vertical lines (both with undefined slope), such as x = 1 and x = 4, are also parallel.

Be careful with the “distinct” part: if two equations have the same slope and the same intercept, they are the same line, not parallel lines — they overlap everywhere instead of never meeting.