Find the equation of the line which passes through $(0, 0)$ with slope $m$.

The number of lines that are parallel to $2x + 6y + 7 = 0$ and have an intercept of length $10$ between the coordinate axes is

Three points $P(h, k)$,$Q(x_{1}, y_{1})$ and $R(x_{2}, y_{2})$ lie on a line. Show that $(h-x_{1})(y_{2}-y_{1}) = (k-y_{1})(x_{2}-x_{1})$.

$A$ ray of light coming from the point $(2, 2\sqrt{3})$ is incident at an angle $30^{\circ}$ with the normal to the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets the $x$-axis at the point $B$. Then,the line $AB$ passes through the point

Find the slope of the line,which makes an angle of $30^{\circ}$ with the positive direction of the $y$-axis measured anticlockwise.

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by: