Find the general equation of a line perpendicular to $x + y + 4 = 0$ and passing through the point $(1, 2)$.

$A$ line $AB$ passes through the origin $(0, 0)$ and is perpendicular to the line $CD$ given by $3x + 4y + 6 = 0$. The equation of line $AB$ is:

In what ratio is the line segment joining the points $(-1, 1)$ and $(5, 7)$ divided by the line $x + y = 4$?

If the straight line $ax + by + c = 0$ always passes through $(1, -2),$ then $a, b, c$ are

The equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

What are the coordinates of a point on the line $2x + 3y + 7 = 0$ which is at a distance of $3$ units from the point $(1, -3)$?