Find the equation of the line passing through the point $(-2, 3)$ with a slope of $-4$.

The equation of the lines on which the perpendiculars from the origin make a $30^\circ$ angle with the $x$-axis and which form a triangle of area $\frac{50}{\sqrt{3}}$ with the axes,are

Find the ratio in which the line joining points $A(-1, -1)$ and $B(2, 1)$ divides the line segment joining points $C(3, 4)$ and $D(1, 2)$.

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

$A$ line $L$ intersects the lines $3x - 2y - 1 = 0$ and $x + 2y + 1 = 0$ at the points $A$ and $B$. If the point $(1, 2)$ bisects the line segment $AB$ and $\frac{x}{a} + \frac{y}{b} = 1$ is the equation of the line $L$,then $a + 2b + 1 = $

$A$ line is perpendicular to the line $ax + by + c = 0$ and passes through $(a, b)$. The equation of the line is