If the points (2,3),(−5,6)  are to be on the opposite side of the line 2x−3y+k=0  then

Let A(2,3),B(−5,6) are two points                L=2x-3y+k=0                 ⇒ L11=4−9+k  = k- 5                               and   L22=−10−18+k =k-28         since A,B are on opposite sides of straight line   ⇒L11 , L22 have opposite signs ,so L11·L22<0 ⇒  k-5k-28<0                  ⇒  5