$A$ straight line makes an angle of $135^\circ$ with the $x$-axis and cuts the $y$-axis at a distance of $-5$ from the origin. The equation of the line is

Find the equation of the line which passes through $(2, 2\sqrt{3})$ and is inclined with the $x-$axis at an angle of $75^{\circ}$.

In the equation $y - y_1 = m(x - x_1)$,if $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$,then

Find the equation of the line passing through the point $(-1, 2)$ and parallel to the line $3x - 4y + 5 = 0$.

$A$ line through the point $A(2,0)$ which makes an angle of $30^{\circ}$ with the positive direction of $x$-axis is rotated about $A$ in clockwise direction through an angle $15^{\circ}$. Then the equation of the straight line in the new position is

The points $(1, 3)$ and $(5, 1)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $y = 2x + c$. Then the value of $c$ is: