Question

Find the line passing through the point $(2,3)$ and perpendicular to the straight line $4x-3y=10$ ?

Answer 1

Let the equation of line be:

$y=mx+c⟶\left(1\right)$

also the equation of straight line is given as:

$4x-3y=10\Rightarrow y=\frac{4}{3}x-\frac{10}{3}where,m^{\prime }=\frac{4}{3}$

since the line in equation $\left(1\right)$ is perpendicular to the given straight line

$\therefore m=-\frac{1}{m^{\prime }}\Rightarrow m=-\frac{3}{4}$

also the line passes through the point $(2,3)$

hence from $\left(1\right)$

$3=(-\frac{3}{4}).2+c\Rightarrow c=\frac{9}{2}$

putting the value of m and c in equation $\left(1\right)$

$y=-\frac{3}{4}x+\frac{9}{2}\Rightarrow 3x+4y=18$

is the required equation