设直线与椭圆交点坐标为（x1,y1）（x2,y2）,则
x1²/36+y1²/24=1 x2²/36+y2²/24=1
两个式子相减得到(x1+x2)(x1-x2)/36+(y1+y2)(y1-y2)/24=0
∴(y1-y2)/(x1-x2)= - 24(x1+x2)/36(y1+y2)
∵x1+x2=6 y1+y2=-2
∴k=(y1-y2)/(x1-x2)=2
∴直线方程为y+1=2(x-3),即2x-y-7=0