Question

Find the equation of the line which passes through the point $(3,4)$ and is such that the portion of it intercepted between the axes is divided by the point in the ratio $2:3$.

Answer 1

Let the equation be $y=mx$

Now if intersects $x$ axis at $(\frac{-c}{m},0)$ and $y$ axis at $(0,c)$

Now if this line divided in ratio $2:3$ we get

$x=\frac{-2c/m+0}{5}=\frac{-2c}{5m}=3$

So, $-2c=15m$

Also $y=\frac{3c}{5}=4⟹c=\frac{20}{3}$

So, $-2c=15m⟹m=\frac{-40}{45}$

So, the line is $y=\frac{-40}{45}x+\frac{20}{3}$