Write a perpendicular equation?

Question

I somewhat know how to write equations that are parallel to a given line with point, but im kind of confused as to what the difference is when writing it as perpendicular.  The question is:

 

Write an equation of the line containing the given point and perpendicular to the given line.  Express your answer in slope-intercept form.

 

(6,7); 6x+y=8

Answer 1

6x+y=8

y=-6x+8, where the slope is -6

the line perpendicular to this line has a slope that is the negative reciprocal of -6

the negative reciprocal is 1/6

y=(1/6)x+b and it goes through (6,7)

7=(1/6)(6)+b

7=1+b

6=b

y=(1/6)x+6 is the line