If the intercept made by the line between the axes is bisected at the point $(5, 2)$,then its equation is

The equation of the line passing through $(1, 1)$ and parallel to the line $2x + 3y - 7 = 0$ is

$A$ line passing through the point $A(-5, -4)$ intersects the lines $x + 3y + 2 = 0$,$2x + y + 4 = 0$,and $x - y - 5 = 0$ at points $B$,$C$,and $D$ respectively. If $\left( \frac{15}{AB} \right)^2 + \left( \frac{10}{AC} \right)^2 = \left( \frac{6}{AD} \right)^2$,find the equation of the line.

$A$ line passes through $P(-4, 1)$ and meets the coordinate axes at points $A$ and $B$. If $P$ divides the segment $AB$ internally in the ratio $1:2$,then the equation of the line is

The equation of the line bisecting the join of $(3, -4)$ and $(5, 2)$ and having its intercepts on the $x$-axis and the $y$-axis in the ratio $2 : 1$ is

Find the equation of a line drawn perpendicular to the line $\frac{x}{4}+\frac{y}{6}=1$ through the point where it meets the $y-$ axis.