Question

Equation of the line which is perpendicular to $9x-5y+6=0$and passing through $(-6,6)$ is

• A. $9x-5y+9=0$
• B. $5x+9y-24=0$
• C. $5x+9y=24$
• D. $5x+9y+13=0$

Answer 1

Answer: (B)

$5x+9y-24=0$

Given,a line ${}^{\prime }{1}^{\prime }$

$1:9x-5y+6=0\Rightarrow 5y=9x+6\Rightarrow y=\frac{9}{5}x+\frac{6}{5}$

Slope of the above line is $m_1=\frac{9}{5}$

Let the slope of the line perpendicular to the above line be $m_2$.Then using the condition for perpendicularity we can write.

$m_1.m_2=-1\Rightarrow \frac{9}{5}.m_2=-1\Rightarrow m_2=\frac{-5}{9}$

$\therefore$ The equation of the line slope $\frac{-5}{9}$ and passing through $(-6,6)$ will be given by

$(y-6)=\frac{-5}{9}(x+6)\Rightarrow 9y-54=-5x-30\Rightarrow 5x+9y-24=0$.