Find the equations of the straight lines which pass through the origin and trisect the portion of the straight line `2x+3y=6` which is intercepted between the axes.

Explanation

Given equation in intercept form is `\frac{x}{3}+\frac{y}{2}=1`

Therefore, its x- intercept is `3` and y- intercept is `2`

`\implies A(3,0)` and `B(0,2)` is on the given line.

And the required line is trisecting the given line between the axes which means it cut the line joining `A(3,0)` and `B(0,2)` in the ratio `2:1`.

By section formula, intersecting point of the given line and the required line is,

`=(\frac{2\times3+1\times0}{3},\frac{2\times 0+1\times 2}{3})`

`=(2,\frac{2}{3})`

Thus, required line passes through the points `(0,0)` and `(2,\frac{2}{3})`

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