AB的斜率是-1/(5-a),BC的斜率是(2a-1)/(-9),A,B,C共线,则-1/(5-a)＝(2a-1)/(-9),解得a=2或7/2.所以斜率为-1/(5-a)=-1/3或-2/3.
所以直线方程是y-1=-1/3(x-5)或y-1=-2/3(x-5),整理得x+3y=8或2x+3y=13.