Determine the equation of the line the portion of which, intercepted by the axes, is divided by the point $(-5,4)$ in the ratio of $1:2$.

Question

Determine the equation of the line the portion of which, intercepted by the axes, is divided by the point $(-5,4)$ in the ratio of $1:2$.

My Attempt: Let the equation of straight line be $$ax+by+c=0$$ It passes through the point $(-5,4)$. $$-5a+4b+c=0$$

Answer 1

Let the equation be $$\dfrac xa+\dfrac yb=1$$

So, $(a,0);(0,b)$ is divided in $1:2$ at $(-5,4)$

i.e., $-5=\dfrac{a\cdot2+0\cdot1}{2+1}$ etc.

Answer 2

HINT: make the Ansatz $$y=mx+n$$ since $P(-5,4)$ is situated on the line we have $$y=m(x+5)+4$$ and the intersection Point withe the $x$ axes is $$P_x(-5-\frac{4}{m};0)$$ and the y-axes $$P_y(0;5m+4)$$ Now must $$\frac{P_xP}{PP_y}=\frac{1}{2}$$ can you finish?