The equation of the straight line passing through the point $(3, 2)$ and perpendicular to the line $y = x$ is

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 equation of the line,where the length of the perpendicular segment from the origin to the line is $4$ and the inclination of this perpendicular segment with the positive direction of the $X$-axis is $30^{\circ}$,is:

Find the equation of the line which passes through $(0, 0)$ with slope $m$.

The equation of the line passing through the point $(1, 2)$ and perpendicular to the line $x + y + 1 = 0$ is

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