The equation of the line parallel to $x/a + y/b = 1$ and passing through $(a, b)$ is .....

The point $P(a, b)$ lies on the straight line $3x + 2y = 13$ and the point $Q(b, a)$ lies on the straight line $4x - y = 5$. Then the equation of the line $PQ$ is

If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of $15^{\circ}$,then the equation of the line in the new position is

In what direction should a line be drawn through the point $(1, 2)$ so that its point of intersection with the line $x + y = 4$ is at a distance of $\frac{\sqrt{6}}{3}$ from the given point (in $^\circ$)?

If the slope of the line $ax + (3 - a)y + 7 = 0$ is $7$,then the value of the integral part of '$a$' is

Find the equation of the line which passes through $(2, 2\sqrt{3})$ and is inclined with the $x-$axis at an angle of $75^{\circ}$.