Find the equation of the line which intersects the $x$-axis at a distance of $3$ units to the left of the origin with a slope of $-2$.

The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

Find the equation of the line that bisects the line segment joining the points $(5, 3)$ and $(4, 4)$ and makes an angle of $45^{\circ}$ with the positive direction of the $x$-axis.

$A$ line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive $x$-axis. Let this line be rotated about the point $P$ through an angle $\frac{\alpha}{2}$ in the clockwise direction. If in the new position,the slope of the line is $2-\sqrt{3}$ and its distance from the origin is $\frac{1}{\sqrt{2}}$,then the value of $3a^2 \tan^2 \alpha - 2\sqrt{3}$ is

If the slope of a straight line passing through $A(3, 2)$ is $3/4$,then the coordinates of the two points on the same line that are $5$ units away from $A$ are

Find the equation of the line that makes an angle of $60^{\circ}$ with the $x$-axis and intersects the $y$-axis at the point $(0, -2)$.