The equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is ______.

2y - 3x = 0

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3y + 2x = 0

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2y + 3x = 0

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3y - 2x = 0

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Solution

The correct option is A
2y - 3x = 0

Given, equation of the straight line, $2 x + 3 y - 7 = 0$
$3 y = - 2 x + 7 y = \frac{- 2}{3} x + \frac{7}{3}$
Comparing the above equation with the slope intercept form of line $y = m_{1} x + c$ , where m is the slope of the line we get, $m = \frac{- 2}{3}$

Product of slopes of perpendicular lines is -1.
So, $m_{1} m_{2} = - 1 \frac{- 2}{3} m_{2} = - 1 m_{2} = \frac{3}{2}$
$∴$ Slope of the required line is $\frac{3}{2}$ .

Equation of line passing through (0, 0) and having slope $\frac{3}{2}$ is $y - y_{1} = m (x - x_{1})$ .

$\Rightarrow y = \frac{3}{2} x$

$= 2 y - 3 x = 0$

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