## Line given by a bi-section

Find the equation for a line $$\pi$$, s.s. the segment between the Cartesian axes is split by the point $$A=(2{,}6)$$ into two parts in ratio 1:2.
By the similartity of triangles follows, that $$\pi$$ intersects axes either in points $$(3{,}0)$$ and $$(0{,}18)$$ or in points $$(6{,}0)$$ and $$(0{,}9)$$. The first pair of intersections yields equation $$x/3+y/18-1=0$$, the second $$x/6+y/9-1=0$$.
There are two possible solutions: $$\pi_1: 9x+y=18$$, and $$\pi_2: 3x+2y=18$$