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

Let the equation of the line be

As P trisects the line AB, therefore, coordinates of P are

Similarly, Q also trisects the line AB. Therefore, coordinates of Q are

Thus, equation of line OP is given by

∴**x - 3y = 0.....(1)**

Equation of line OQ is given by

∴**4x - 3y = 0.....(2)**

Lines (1) and (2) pass through the origin and trisect the portion of the line *2x + 3y = 6*.

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