Definition:Point at Infinity

Definition
Let $\LL_1$ and $\LL_2$ be straight lines embedded in a cartesian plane $\CC$, given by the equations:

Let $l_1 m_2 = l_2 m_1$, thus by Condition for Straight Lines in Plane to be Parallel making $\LL_1$ and $\LL_2$ parallel.

In this case the point of intersection of $\LL_1$ and $\LL_2$ does not exist.

However, it is convenient to define a point at infinity at which such a pair of parallel lines hypothetically "intersect".