Find the equation of the line passing through the point $(3, 4)$ and making intercepts on the axes of equal magnitude but opposite signs.

Find the value of $k$ for which the line $(k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0$ passes through the origin.

$A$ line passing through the point $A(9,0)$ makes an angle of $30^{\circ}$ with the positive direction of $x$-axis. If this line is rotated about $A$ through an angle of $15^{\circ}$ in the clockwise direction,then its equation in the new position is

The intercept cut off from the $y$-axis is twice that from the $x$-axis by a line,and the line passes through $(1, 2)$. Find its equation.

The equation of the line parallel to the line $3x - 4y + 2 = 0$ and passing through $(-2, 3)$ is

The points $A (1, 3)$ and $C (5, 1)$ are the opposite vertices of a rectangle. The equation of the line passing through the other two vertices and having a gradient of $2$ is: