Question

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

• A. 2y - 3x = 0
• B. 3y + 2x = 0
• C. 2y + 3x = 0
• D. 3y - 2x = 0

Answer 1

The correct option is A

2y - 3x = 0

Slope of straight line $2x+3y-7=0$ is

$\text{Slope}=-\left(\frac{\text{coefficient of x}}{\text{coefficient of y}}\right)$

= $\frac{-2}{3}$

We know, product of slopes of perpendicular lines is -1

$\therefore \text{Slope of the required line is}\frac{3}{2}$

Equation of line passing through (0,0) and having slope $\frac{3}{2}$ is

$y-y_1=m(x-x_1)$

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

$\Rightarrow 2y-3x=0$