The equation of a line passing through $(3, -4)$ and perpendicular to the line $3x + 4y = 5$ is

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:

$A$ straight line through the point $P(1, 2)$ makes an angle $\theta$ with the positive $X$-axis in the anticlockwise direction and meets the line $x + \sqrt{3}y - 2\sqrt{3} = 0$ at $Q$. If $PQ = \frac{1}{2}$,then $\theta =$

If the line passing through $(4, 3)$ and $(2, k)$ is perpendicular to the line $y = 2x + 3$,then the value of $k$ is:

Find the equation of the line,which makes intercepts $-3$ and $2$ on the $x$- and $y$-axes respectively.

Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is: