find the equation of the straight line passing through `(2,1)` and bisecting the portion of the straight line `3x-5y=15` lying between the axes.

Explanation

Given equation in intercept form is `\frac{x}{5}-\frac{y}{3}=1`

Therefore, its x- intercept is `5` and y- intercept is `-3`

`\implies A(5,0)` and `B(0,-3)` is on the given line.

And the mid point of the these two points lie on the required line.

Midpoint of AB `=(\frac{5}{2},\frac{-3}{2})`

Thus, required line passes through the points `(2,1)` and `(\frac{5}{2},\frac{-3}{2})`

Hence, the required equation is, `y-1=\frac{\frac{-3}{2}-1}{\frac{5}{2}-2}(x-2)`

`\implies y-1=-5(x-2)`

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