Step-by-step explanation:
Equation of the given line is :
[tex] 2x +12y= - 1\\
\therefore 12y = - 2x - 1\\
\therefore y = \frac {- 2}{12}x - \frac {1}{12}\\
\therefore y = - \frac {1}{6}x - \frac {1}{12}\\[/tex]
Equating above equation with [tex] y= m_1x + c
[/tex] we find:
[tex] m_1 = - \frac{1}{6}[/tex]
Where [tex] m_1[/tex] is the slope of given line:
Let the slope of required line be [tex] m_2.[/tex]
Since lines are perpendicular
[tex] \therefore m_1 \times m_2= - 1\\
\\\therefore - \frac{1}{6} \times m_2= - 1\therefore m_2= 6\\[/tex]
Equation of required line in slope point form is given as:
[tex] y-y_1 =m_2(x-x_1) \\
\therefore y-9 =6(x-0)\\
\therefore y-9 =6x\\
\huge\orange {\boxed {\therefore y =6x+9}} \\[/tex]
