The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

If the line $6x - 7y + 8 + \lambda(3x - y + 5) = 0$ is parallel to the $y$-axis,then $\lambda$ is equal to

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 line $L_1$ passes through the points $(-1, 2)$ and $(3, 6)$. If $L_1$ divides the line $L_2$ (which passes through $(3, -1)$) in the ratio $1:3$ internally, and the point of intersection lies on $L_1$, find the equation of $L_2$ given that it is perpendicular to $L_1$.

Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $y$-intercept is $-\frac{3}{2}$.

$A$ line is perpendicular to the line $ax + by + c = 0$ and passes through $(a, b)$. The equation of the line is