Question

write an equation of the line contacting the points (5,-6) and perpendicular to the line 6x-y=4

Answer 1

y + 6 = -1/6 ( x - 5 )

That is point-slope form. :) (its called something like that)
6x-y=4 is the same as y=6x-4 the slope of that line is 6, so a perpendicular line would be -1/6.