If the line $2x+3y=5$ denoted by $\text{'}L\text{'}$ then the points $\left(1,2\right)\left(3,4\right)$ is

$L=2x+3y-5=0$ 

$L_{11}= L_{\left(1,2\right)}=2+6-5=3>0$

$L_{22}= L_{\left(3,4\right)}=6+12-5=13>0$

  both will have same sign ,so they  lie on same side of $L=0$