Find the angle between the $x$-axis and the line joining the points $(3, -1)$ and $(4, -2).$ (in $^{\circ}$)

Find the equation of the line which passes through the point $(-4, 3)$ with slope $\frac{1}{2}$.

The slope of the line passing through the origin,which makes an angle of $30^{\circ}$ with the positive direction of the $Y$-axis measured anticlockwise,is

The equations of the sides $AB$,$AC$,and $BC$ of a $\triangle ABC$ are respectively $x-3y=0$,$3x-y=0$,and $x+y+4=0$. If $P$ and $Q$ are points on the line $3x-y+k=0$ passing through $B$ such that $PB:BQ=1:1$,then $k=$

Show that two lines $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,where $b_{1}, b_{2} \neq 0$,are parallel if $\frac{a_{1}}{b_{1}} = \frac{a_{2}}{b_{2}}$.

If the slope of a line passing through the point $A(3, 2)$ is $3/4$,then the points on the line which are $5$ units away from $A$ are: