Question

Find the equation of the line that is parallel to $2x+5y-7=0$ and passes through the mid-point of the line segment joining the points $(2,7)$ and $(-4,1)$.

Answer 1

$2x+5y+c=0$ is the required equation of line parallel $2x+5y-7=0$

Mid point of two points $(2,7)$ and $(-4,1)$ is $\Rightarrow (\frac{2+(-4)}{2},\frac{7+1}{2})$

$\Rightarrow (-1,4)$
Substitute $(x,y)=(-1,4)$ in equation $2x+5y+c=0$, we get

$2(-1)+5\left(4\right)+c=0$
$-2+20+c=0$
$c=-18$

$\therefore$ equation of line parallel $\Rightarrow 2x+5y-18=0$