Question

Find the equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0.
$\left[2Marks\right]$

Answer 1

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

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

= $\frac{-2}{3}$
$\left[1Mark\right]$

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

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

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

$\Rightarrow 2y-3x=0$
$\left[1Mark\right]$