Find the equation of the line which passes through the point $(-4, 3)$ with slope $\frac{1}{2}$.

If the line passing through $(4, 3)$ and $(2, k)$ is perpendicular to the line $y = 2x + 3$,then the value of $k$ is:

The equation of the straight line passing through $(-a, 0)$ and forming a triangle with the coordinate axes of area $T$ is

The equation of a line with slope $-\frac{1}{\sqrt{2}}$ and making an intercept of $2 \sqrt{2}$ units on the negative direction of the $y$-axis is:

Find the equation of a line passing through the point $(2, 5/3)$ such that the segment of the line intercepted between the axes is divided by the point in the ratio $5 : 4$.

$A$ straight line parallel to the line $y=\sqrt{3}x$ passes through $Q(2,3)$ and cuts the line $2x+4y-27=0$ at $P$. Then the length of the line segment $PQ$ is