Question

Show that the straight lines 3 x minus 5 y + 7 is equal to zero and 15 x + 9 y + 4 is equal to zero are perpendicular

Answer 1

$\textbf{Concept:}$

$\text{Slope of the straight line ax+by=c=0 is \bf\frac{-a}{b} }$

$\text{Given lines are}$

$\textbf{3x-5y+7=0 and 15x+9y=4=0}$

$\text{Slope of 3x-5y+7=0 is }m_1=\frac{-3}{-5}=\frac{3}{5}$

$\text{Slope of 15x+9y+4=0 is }m_2=\frac{-15}{9}=\frac{-5}{3}$

$\text{Now,}$

$m_1{\times}m_2$

$=\frac{3}{5}{\times}\frac{(-5)}{3}$

$=-1$

$\therefore\textbf{The given lines are perpendicular}$