$A$ straight line makes an angle of $135^\circ$ with the $x$-axis and cuts the $y$-axis at a distance of $-5$ from the origin. The equation of the line is

The ends of the base of an isosceles triangle are at $(2a, 0)$ and $(0, a)$. The equation of one side is $x = 2a$. The equation of the other side is

$A$ 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

Consider the following population and year graph (Fig.),find the slope of the line $AB$ and using it,find what will be the population in the year $2010$?

$A$ man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A, B$ and $C$ are placed at the points $(1,1), (2,2)$ and $(4,4)$ respectively. Which of these stones is/are on the path of the man?

Find the equation of the line passing through the point $(4, 3)$ such that the sum of its intercepts on the axes is $-1$.