If two lines intersect, then there are two possibilities
1) The lines intersect at exactly one point. This happens if the slopes of the two lines are different (the y-intercepts may or may not be the same).
2) The lines intersect at infinitely many points. This happens when both slopes are the same and when both y-intercepts are the same. In short, the two equations are identical. Often they may be written in different forms. For example, the equation y = 2x+1 and 2y = 4x+2 are the same equation. Divide everything in equation (2) by 2 and you'll get equation (1).
