A fixed point A(3,−1) is given. Let B(t,5) be a variable point on the vertical line x=t, where t is a real number.
a. (i) Obtain the slope of the line AB in terms of t.
b. (ii) The straight line L is given by 2x−y+4=0. Determine the slope of L.
c. (iii) Find the value of t for which the line AB is perpendicular to L.
d. (iv) For the value of t obtained in part (iii), write the equation of the line AB in slope–intercept form.