Equation of Straight Line through Intersection of Two Straight Lines/Also presented as

Theorem

Let $u = l_1 x + m_1 y + n_1$.

Let $v = l_2 x + m_2 y + n_2$.

Let $\LL_1$ be defined by the equation $u = 0$.

Let $\LL_2$ be defined by the equation $v = 0$.

Then the equation of the straight line passing through the point of intersection of $\LL_1$ and $\LL_2$ can be written as:

$u - k v = 0$

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $10$. Equation of a straight line through the intersection of two given lines