Question

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

Answer 1

Given a line is perpendicular to the line $4x-3y=10$ .... $\left(i\right)$ and passing through $(2,3)$

Now, slope of the above line $\left(i\right)$ is $m=\frac{4}{3}$

Let the slope of perpendicular line be $m_1$

then $m_{1}m=-1$

$\Rightarrow m_1=\frac{-3}{4}$

Then the equation with slope will be $y=\frac{-3}{4}x+c$

The above line is passing through $(2,3)$

$\Rightarrow 3=\frac{-3}{4}\times 2+c$

$\Rightarrow c=\frac{9}{2}$

Therefore the required equation of line is $y=\frac{-3}{4}x+\frac{9}{2}$

$4y+3x=18$