Prove that nonvertical lines are parallel if and only if their slopes are equal.
Lines can be written in the form , where is the gradient and is the intercept.
So we could write the equation of two lines as
and .
You should know that parallel lines never cross. These two lines will cross when their equations are equal. So
.
Obviously there is no solution when the denominator is , in other words, where .
So the only time when there will not be a point of intersection is when the two gradients are equal.
In other words, the lines are parallel when their gradients are equal.