Find the slope of the line passing through the points $(3, -2)$ and $(-1, 4)$.

In what direction should a line be drawn through the point $(1, 2)$ so that its point of intersection with the line $x + y = 4$ is at a distance of $\frac{\sqrt{6}}{3}$ from the given point (in $^\circ$)?

If a straight line through the point $P(1, 2)$,which makes an angle $45^{\circ}$ with the $X$-axis,meets the line $3x + 4y + 5 = 0$ at $Q$,then the length of $PQ$ equals ......... units.

The length of the perpendicular from the origin to a line is $9$ and the perpendicular makes an angle of $120^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.

If two vertical poles of heights $20\,m$ and $80\,m$ stand apart on a horizontal plane,then the height (in $m$) of the point of intersection of the lines joining the top of each pole to the foot of the other is:

The equation of the straight line which passes through the point $(1, -2)$ and cuts off equal intercepts from the axes is: