Question

A given line has the equation 2x+12y=-1.

Answer 1

2x+12y=-1
y = -1x/6 -1/12

Perpendicular lines are lines that cross one another at a 90° angle. They have slopes that are opposite reciprocals of one another. Therefore, the slope of the perpendicular line in this problem is the opposite reciprocal of -1/6 which is 6. The equation would be 

y=(6)x+9

Answer 2

Answer:

$y = 6x+9$

Step-by-step explanation:

Point slope form:

The equation of line passes through the point $(x_1, y_1)$ is given by:

$y-y_1=m'(x-x_1)$                 ....[1]

where, m' is the slope

As per the statement:

A given line has the equation

2x+12y=-1

Subtract 2x from both sides we have;

$12y =-2x-1$

Divide both sides by 12 we have;

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

On comparing with slope intercept form equation y=mx+b we get;

$m= -\frac{1}{6}$

We have to find the equation in slope intercept form, of the line that is perpendicular to the given line and passes through the point (0,9)

Since, a line is perpendicular to a given line.

⇒ $m \times m' =-1$

⇒$m'= \frac{-1}{m}$

⇒$m' = \frac{-1}{\frac{-1}{6}}$

Simplify:

m' = 6

Substitute the value of m' and (0, 9) in [1] we have;

$y-9 =6(x-0)$

⇒$y-9 = 6x$

Add 9 to both sides we have;

$y = 6x+9$

Therefore, the equation in slope intercept form, of the line that is perpendicular to the given line and passes through the point (0,9) is, $y = 6x+9$