Question

Prove that the lines $2x+3y=19$ and $2x+3y=-7$ are equidistant from the line $2x+3y=6$.

Answer 1

All the three lines are parallel. Any point on the third line on putting $x=0$ is $(0,2)$. Its distance from the other two lines are
$\frac{0+6-19}{\surd \left(13\right)}=-\sqrt{13}$ and $\frac{0+6-7}{\surd \left(13\right)}=\sqrt{13}$
Above shows that these lines are equidistance from the third line and on opposite sides of it.