The equation of the line making an angle of $135^\circ$ with the positive $x$-axis and having a $y$-intercept equal to $-2$ is:

Find the equation of the line passing through the point $(0, 2)$ making an angle of $\frac{2 \pi}{3}$ with the positive $x$-axis. Also,find the equation of the line parallel to it and crossing the $y$-axis at a distance of $2$ units below the origin.

The equation of the line parallel to $x/a + y/b = 1$ and passing through $(a, b)$ is .....

If $\alpha$ is the angle made by the perpendicular drawn from the origin to the line $12x - 5y + 13 = 0$ with the positive $X$-axis in the anti-clockwise direction,then $\alpha =$

The angles made with the $X$-axis by the two lines passing through the point $P(1, 2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

The line $(3x - y + 5) + \lambda (2x - 3y - 4) = 0$ will be parallel to the $y$-axis,if $\lambda$ =