The equation of the line passing through $(1, 1)$ and parallel to the line $2x + 3y - 7 = 0$ is

The line joining the points $(-1, 3)$ and $(4, -2)$ will pass through the point $(p, q)$ if

The equation of the line,which bisects the line segment joining the points $(2, -19)$ and $(6, 1)$ and is perpendicular to the line joining the points $(-1, 3)$ and $(5, -1)$,is

The area of a triangle formed by a line with the coordinate axes is $49 \text{ sq. units}$. If the perpendicular drawn from the origin to this line makes an angle of $45^\circ$ with the positive $X$-axis, then the equation of the line is:

The line passing through $(-1, \pi/2)$ and perpendicular to $\sqrt{3} \sin \theta + 2 \cos \theta = \frac{4}{r}$ is

The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is