2x+y-8=0 .....(1)
x-2y+1=0 ......(2)
(1)*2 +(2)得:5x-15=0,x=3
y=8-2x=2
交点(3,2)
令斜率为k,根据点斜式:y=k(x-3)+2
令y=0,得x=3-k/2
令x=0,得y=-3k+2
与坐标轴围成三角形面积1/2:
1/2 * |3-2/k| * |-3k+2| = 1/2
|(3-2/k)(3k-2)| = 1
9k-12+4/k=±1
9k-12+4/k=-1时:
9k²-11k+4=0,判别式<0,无解
9k-12+4/k=1时:
9k²-13k+4=0
(9k-1)(k-4)=0
k=1/9,或k=4
k=1/9时,y=1/9(x-3)+2 = 1/9x+5/3
k=4时,y=4(x-3)+2 = 4x+10