Question

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)

Answer 1

Answer: A. Y= -6x+9

Explanation:

Answer 2

Explanation:

Equation of the given line is :

`2x +12y= - 1\\</p><p>\therefore 12y = - 2x - 1\\</p><p>\therefore y = \frac {- 2}{12}x - \frac {1}{12}\\</p><p>\therefore y = - \frac {1}{6}x - \frac {1}{12}\\`

Equating above equation with
`y= m_1x + c</p><p>` 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\\</p><p>\\\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) \\</p><p>\therefore y-9 =6(x-0)\\</p><p>\therefore y-9 =6x\\</p><p>\huge\orange {\boxed {\therefore y =6x+9}} \\`