The equation of the straight line which passes through the point `(-4,3)` such that the portion of the line between the axes is divided internally be the point in the ratio `5:3` is `9x-20 y+96=0` `9x+20 y=24` `20 x-9y+53=0` none of these

Explanation

Let the line cut the x axis at `(a,0)` and y−axis at `(0,b)`.

Therefore
It is given that the point` (−4,3)` divides the line internally in 5:3 ratio.

Hence applying the formula for internal division of line segment, we get

`3a/8​=−4 and 5b/4​=3`
Hence `a=(−32)/3​ `and `b=(24)/5`
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Using slope intercept form we get

`x/(−32/3)​​+y/(24/5)​​=1
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