The equations of the line passing through origin and passing through $(2, 3)$ is

2 x + 3 y = 0

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2 x - 3 y = 0

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3 x + 2 y = 5

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N o n e o f t h e s e

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Solution

The correct option is D $N o n e o f t h e s e$
The slope of the equation of the line that passes through them is $\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{3 - 0}{2 - 0} = \frac{3}{2}$

General equation of line is given as,

$\Rightarrow$ $y - y_{2} = m (x - x_{2})$

$\Rightarrow$ $(y - 3) = \frac{3}{2} (x - 2)$

$\Rightarrow$ $2 y - 6 = 3 x - 6$

$\Rightarrow$ $3 x - 2 y = 0$

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