Find the equation of the line passing through the point $(1, -2)$ and making equal intercepts on the axes.

$A$ line is perpendicular to the line $ax + by + c = 0$ and passes through $(a, b)$. The equation of the line is

Find the $y$-intercept of a line that is perpendicular to $3x + y = 3$ and passes through the point $(2, 2)$.

$A$ line passing through the point $A(9,0)$ makes an angle of $30^{\circ}$ with the positive direction of $x$-axis. If this line is rotated about $A$ through an angle of $15^{\circ}$ in the clockwise direction,then its equation in the new position is

The line $PQ$ with equation $x - y = 2$ intersects the $x$-axis at $P$. Given $Q$ is $(4, 2)$. Find the equation of the line $PQ$ after it is rotated by $45^{\circ}$ in the counter-clockwise direction about point $P$.

The equation of the line,which bisects the line segment joining the points $(2, -19)$ and $(6, 1)$ and is perpendicular to the line joining the points $(-1, 3)$ and $(5, -1)$,is