The equation of the perpendicular to the line $2 x - 3 y + 5 = 0$ and making an intercept $3$ with $y$ -axis is :

3 x + 2 y - 6 = 0

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3 x + 2 y - 12 = 0

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3 x - 2 y - 6 = 0

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3 x + 2 y + 6 = 0

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3 x + 2 y - 5 = 0

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Solution

The correct option is A $3 x + 2 y - 6 = 0$
Given equation of line is $2 x - 3 y + 5 = 0$
The slope of the given line is $\frac{2}{3}$ .
Therefore, the slope of the perpendicular to the given line is $m = - \frac{3}{2}$ .
Also, line intercepty-axis $= 3,$ i.e., $c = 3$ .
We know $y = m x + c$
Therefore, $y = - \frac{3}{2} x + 3$
$\Rightarrow 3 x + 2 y - 6 = 0$

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