A straight line L is given by (k+3)x−(2k−1)y+4=0, where k is a real parameter. Another line M has the equation 5x+10y−15=0. Point P(2,−1) lies in the plane.
(i) Find all values of k for which the line L passes through the point P.
(ii) For each value of k obtained in part (i), rewrite L in slope-intercept form and hence state its slope m1.
(iii) Rewrite M in slope-intercept form and state its slope m2.
(iv) For each admissible value of k, determine whether L is parallel to M, perpendicular to M, or neither. Give reasons based on the slopes obtained.