What is the equation of a line that passes through the point (6,1) and is perpendicular to the line whose equation is y=-2x-6?

When you want a line perpendicular to a line you have already... the slope has to be the opposite reciprocal.

example this line y= - 2x - 6
slope is -2 so opposite reciprocal is  1/2

so now we have the slope of the new line m=1/2
 now we use point slope formula with the point (6,1)

y-y1= m (x - x1)      plug and chug
 
y- 1 = (1/2) (x - 6)
y=1/2x-2

hope that helps