Let $PS$ be the median of the triangle with vertices $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is

If the line $px - qy = r$ intersects the coordinate axes at $(a, 0)$ and $(0, b)$,then the value of $(a + b)$ is equal to

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 $-\frac{3}{2}$.

Find the equation of a line that makes an angle of $60^{\circ}$ with the $x$-axis and makes an intercept of $5$ units on the negative direction of the $y$-axis.

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 $^\circ$)?

If a line $L$ passes through the point of intersection of the lines $2x + 3y + 1 = 0$ and $x + y - 3 = 0$ and the angle made by the line $L$ with the $X$-axis measured in the positive direction from the positive $X$-axis is $\tan^{-1} \frac{2}{3}$,then the sum of the intercepts made by this line on the axes is