(2k-1)x-(k+3)y-(k-11)=0

问题描述:

(2k-1)x-(k+3)y-(k-11)=0

证明:当2k-1=0即k=1/2时,
-(1/2 +3)y-(1/2 -11)=0,y=3
当k+3=0即k=-3时,
(-3*2 -1)x -(-3-11)=0,x=2
所以直线必过(2,3)
(2K-1)X-(K+3)Y-(K-11)=0变形为K(2X-Y-1)+(-X+3Y-1)=0.
设直线2X-Y-1=0与-X+3Y-1=0的交点为M(4/5,3/5),则
M点的坐标满足(2K-1)X-(K+3)Y-(K-11)=0.因此不论K为何值,
一次函数(2K-1)X-(K+3)Y-(K-11)=0的图象恒过一定点M.