Find the slope of the line passing through the points $(3, -2)$ and $(-1, 4)$.

The system of linear equations $ax - y + 2 = 0$ and $x + ay + 3 = 0$ has a unique solution. Then,the set of values of $a$ is . . . . . . .

What is the normal form of the line $x + \sqrt{3}y - 4 = 0$?

If the $x-$intercept of some line $L$ is double that of the line $3x + 4y = 12$ and the $y-$intercept of $L$ is half that of the same line,then the slope of $L$ is

The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1, 2)$ and $(-3, 5)$ in the ratio $4:3$ externally is

The equation of the line passing through the origin and the point $(a \cos \theta, a \sin \theta)$ is .....