# Find the equation to the straight line which passes through the point (-5,4)and is such that the portion of it between the axes is divided by the point inthe ratio of 1:2

Let the requried straight line be $\\ x/a +y/b=1$ .this meets the axes in the point whose coordinate are$(a,0);and (0,b)$

The coordinates of the point dividing the line joining these points in the ratio 1:2 , are

$\\ (2\times a+1\times 0)/3 ; and ; (2\times 0+1\times b)/3$

i.e ,$\\2a/3 ; and ; b/3$

if this be the point (-5,4) we have

$\\ -5=2a/3;and; 4=b/3\\ \\\Rightarrow a=-15/2 ; b =12$

The requried straight line is

$\\ \Rightarrow x/-15/2+y/12=1\\ \\\Rightarrow 5y-8x-60=0$

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