Let A(1,4) and B(5,6) be two points in the plane.
a. (i) Find the slope of the line segment AB.
b. (ii) Determine the equation of the line that passes through the point (3,−2) and is perpendicular to AB.
c. (iii) Verify whether the line obtained in part (ii) is parallel to the line 2x+y=0.