Find the equation of the line passing through $(4, 6)$ and parallel to the line $3x - 7y + 2 = 0$.

If the length of the intercept made on the line $y=ax$ by the lines $y=2$ and $y=6$ is less than $5$,then which of the following is true?

The line joining the points $(-1, 3)$ and $(4, -2)$ will pass through the point $(p, q)$ if

The line $L_1$ passes through the points $(-1, 2)$ and $(3, 6)$. If $L_1$ divides the line $L_2$ (which passes through $(3, -1)$) in the ratio $1:3$ internally, and the point of intersection lies on $L_1$, find the equation of $L_2$ given that it is perpendicular to $L_1$.

Find the equation of the line passing through the point $(3, 4)$ and making intercepts on the axes of equal magnitude but opposite signs.

The equation of a line,whose perpendicular distance from the origin is $5$ units and the angle,which the perpendicular to the line from the origin makes,is $210^{\circ}$ with the positive $X$-axis,is