Question

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

Answer 1

Given, equation of the straight line, $2x+3y-7=0$
$3y=-2x+7y=\frac{-2}{3}x+\frac{7}{3}$
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, $m=\frac{-2}{3}$ (1 mark)

Product of slopes of perpendicular lines is -1.
So, $m_1{m}_2=-1\frac{-2}{3}{m}_2=-1m_2=\frac{3}{2}$
$\therefore$ Slope of the required line is $\frac{3}{2}$. (1 mark)

Equation of line passing through (0, 0) and having slope $\frac{3}{2}$ is $y-y_1=m(x-x_1)$.

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

$=2y-3x=0$ (1 mark)