Reduce the following equation into slope-intercept form and find its slope and the $y$-intercept.
$x+7y=0$

Reduce the following equation into intercept form and find its intercepts on the axes: $3y + 2 = 0$.

The line passing through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line passing through the points $(8, 12)$ and $(x, 24)$. Find the value of $x$.

$A$ line $L$ perpendicular to the line $5x - 12y + 6 = 0$ makes a positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is $2$ units and the angle made by the perpendicular drawn from the origin to the line $L$ with the positive $X$-axis is $\theta$,then $\tan \theta + \cot \theta =$

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

$A$ 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