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

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

The line passing through the points $(a, b)$ and $(-a, -b)$ passes through which of the following points?

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

If a straight line passes through the point $(\alpha, \beta)$ and the portion of the line intercepted between the axes is divided equally at that point, then $\frac{x}{\alpha} + \frac{y}{\beta}$ is

Find the equation of a straight line which passes through the point $(-1, -1)$ and makes an angle $150^{\circ}$ with the positive direction of the $X$-axis.