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

The equation of the line passing through $(1, 1)$ and parallel to the line $2x + 3y - 7 = 0$ is

In what ratio is the line segment joining the points $(-1, 1)$ and $(5, 7)$ divided by the line $x + y = 4$?

The equation of the straight line cutting off an intercept of $2$ from the negative direction of the $y$-axis and inclined at $30^\circ$ to the positive direction of the $x$-axis 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 $^\circ$)?

The length of the perpendicular from the origin to a line is $9$ and the perpendicular makes an angle of $120^{\circ}$ with the positive direction of the $y$-axis. Find the equation of the line.