The intercept of a line between the coordinate axes is divided by the point $(-5, 4)$ in the ratio $1 : 2$. The equation of the line will be:

The line passing through $(1, 0)$ and $(-2, \sqrt{3})$ makes an angle of ...... with the $x$-axis. (in $^o$)

If the points $A(5, k)$,$B(-3, 1)$ and $C(-7, -2)$ are collinear,then $k=$

Find the equation of the line such that the perpendicular drawn from the origin to the line makes an angle of $30^{\circ}$ with the $x$-axis and the line forms a triangle of area $\frac{50}{\sqrt{3}}$ with the axes.

In the figure,a time-distance graph of a linear motion is given. Two positions of time and distance are recorded as: when $T = 0, D = 2$ and when $T = 3, D = 8$. Using the concept of slope,find the law of motion,i.e.,how distance depends upon time.

For what values of $a$ and $b$ are the intercepts cut off on the coordinate axes by the line $ax + by + 8 = 0$ equal in length but opposite in sign to those cut off by the line $2x - 3y + 6 = 0$ on the axes?