The equation of straight line which passes through the point (-4,3) such that the portion of the line between the axes is divided by the point in ratio 5:3 is -

Explanation

Let the required equation in intercept form be `\frac{x}{a}+\frac{y}{b}=1`

Therefore, its x- intercept is `a` and y- intercept is `b`

`\implies A(a,0)` and `B(0,b)` is on the given line.

And it is given the point `(-4,3)` divides the line segment `A(a,0)` and `B(0,b)` in the ratio `5:3`.

By section formula,

`(-4,3)=(\frac{5\times0+3\timesa}{8},\frac{5\times b+3\times 0}{8})`

`\implies(-4,3)=(\frac{3a}{8},\frac{5b}{8})`

`\implies 3a=-32` and `5b=24`

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