If the points $A(5, k)$,$B(-3, 1)$ and $C(-7, -2)$ are collinear,then $k=$

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 $k=$

The number of lines passing through $A(3, 4)$ such that the sum of their non-zero intercepts is zero is:

The equation of the line passing through the point $(-3, 1)$ and bisecting the angle between the coordinate axes in the second quadrant is:

The equation $r \cos \left(\theta-\frac{\pi}{3}\right)=2$ represents

The equation of the line perpendicular to $2x - 3y + 5 = 0$ and making an intercept of $3$ with the positive $Y$-axis is