Write the equation of the lines for which $\tan \theta = \frac{1}{2}$,where $\theta$ is the inclination of the line and $x$-intercept is $4$.

The equation of the line which makes a right-angled triangle with the axes whose area is $6$ sq. units and whose hypotenuse is $5$ units,is

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

The $x$-intercept and $y$-intercept of the line $2x - 3y = 6$ are respectively:

Reduce the following equation into intercept form and find its intercepts on the axes: $3y + 2 = 0$.

Let $O=(0,0)$. Let $A$ and $B$ be points on the $X$-axis and $Y$-axis respectively such that $\angle OBA = 60^{\circ}$. Let $D$ be a point in the first quadrant such that $\triangle OAD$ is an equilateral triangle. Then,the slope of $DB$ is