Question

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

• A. $2x+3y=0$
• B. $3x-2y=0$
• C. $y+5=0$
• D. $y-5=0$

Answer 1

The correct option is B $3x-2y=0$

Consider the given equation.

$2x+3y-7=0$ $...........\left(1\right)$

$slope\left(m_1\right)=-\frac{2}{3}$

Since, the line is perpendicular to given line. so slope will be

$slope\left(m_2\right)=-\frac{1}{m_2}=\frac{3}{2}$

We know that the equation of the line which is passing through the point $(0,0)$

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

So,

$y-0=\frac{3}{2}(x-0)$

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

$3x-2y=0$

Hence, this is the answer.