In what ratio does the line $y - x + 2 = 0$ divide the line segment joining the points $(3, -1)$ and $(8, 9)$?

If the $x-$intercept of some line $L$ is double that of the line $3x + 4y = 12$ and the $y-$intercept of $L$ is half that of the same line,then the slope of $L$ is

$PS$ is the median of the triangle with vertices at $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The intercepts on the coordinate axes of the line passing through point $(1, -1)$ and parallel to $PS$ are respectively:

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:

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by:

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.