The line l is represented by 4x−y+9=0. A point R(k,2k) is such that the line through R perpendicular to l passes through the fixed point S(1,−3).
a. (i) Find the slope of l.
b. (ii) Write the general form of the line passing through R and perpendicular to l.
c. (iii) Using the condition that this line also passes through S, determine the possible value(s) of k and hence obtain the required equation(s) of the line(s).