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

The slope-intercept form of a linear equation is:

y = mx +c 


Where 
m = slope
c =  intercept


2x + 12y = −1

12y = -2x – 1

y = -1/6y – 1/12

-----------------------------------------------------
The line that is perpendicular to this line will have a slope = 6


Note: The product of the slopes of two perpendicular lines = -1


Equation of the second line:

y – 9 = 6(x – 0)

y – 9 = 6x

y = 6x + 9

Answer 2

The slope-intercept form of a linear equation is:

y = mx +c 

Where 

m = slope

c =  intercept

2x + 12y = −1

12y = -2x – 1

y = -1/6y – 1/12

-----------------------------------------------------

The line that is perpendicular to this line will have a slope = 6

Note: The product of the slopes of two perpendicular lines = -1

Equation of the second line:

y – 9 = 6(x – 0)

y – 9 = 6x

y = 6x + 9

If there is any confusion please leave a comment below.