Reduce the following equation into slope-intercept form and find its slope and the $y$-intercept.
$x+7y=0$

Find the equation of the line passing through the intersection of the lines $y = 3$ and $x + y = 0$ and parallel to the line $2x - y = 4$.

If the line passing through the points $(4, 3)$ and $(2, \lambda)$ is perpendicular to the line $y = 2x + 3$,then find the value of $\lambda$.

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 polar equation of the line perpendicular to the line $\sin \theta - \cos \theta = \frac{1}{r}$ and passing through the point $\left(2, \frac{\pi}{6}\right)$ is

In what direction should a line be drawn through the point $(1, 2)$ so that its point of intersection with the line $x + y = 4$ is at a distance of $\frac{\sqrt{6}}{3}$ from the given point (in $^\circ$)?