Question

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the y-axis.

Answer 1

The required line is perpendicular to the given line $6x+4y=24$

$\therefore$ (Slope of required line)$\times$ (Slope of given line) = - 1

$m_1=\frac{-1}{\left(\frac{-6}{4}\right)}=\frac{4}{6}$

and

The required line passes through the point $(x_1,y_1)$ where it meets the y-axis

$\therefore$ x coordinates at that point is zero i.e.,

$x_1=0$

$(y-y_1)=\frac{4}{6}(x-0)$

$6y-6y_1=4x$

$2x-3y=-3y_1\Rightarrow y_1=6$

$2x-3y=-18$

$2x-3y+18=0$