Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $x$-intercept is $4$.

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

Find the $y$-intercept of a line that is perpendicular to $3x + y = 3$ and passes through the point $(2, 2)$.

What is the equation of a line parallel to $ax + by + c = 0$ and passing through the point $(c, d)$?

$A$ 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

$A$ line passes through $(x_{1}, y_{1})$ and $(h, k)$. If the slope of the line is $m$,show that $k - y_{1} = m(h - x_{1})$.