A given line has the equation 2x+12y= -1 What is the equation in slope intercept form of the line that is perpendicular to the given line and passes through the point (0,9)

Question

asked Nov 13, 2021 117k views

2 Answers

Nils Magne Lunde · Answer 1 · 2021-11-17T12:49:47+0000

Explanation:

Equation of the given line is :

$2x +12y= - 1\\\therefore 12y = - 2x - 1\\\therefore y = \frac {- 2}{12}x - \frac {1}{12}\\\therefore y = - \frac {1}{6}x - \frac {1}{12}\\$

Equating above equation with
y= m_1x + c we find:

m_1 = - (1)/(6)

Where
m_1 is the slope of given line:

Let the slope of required line be
m_2.

Since lines are perpendicular

$\therefore m_1 * m_2= - 1\\\\\therefore - (1)/(6) * m_2= - 1\therefore m_2= 6\\$

Equation of required line in slope point form is given as:

$y-y_1 =m_2(x-x_1) \\\therefore y-9 =6(x-0)\\\therefore y-9 =6x\\\huge\orange {\boxed {\therefore y =6x+9}} \\$