What is the equation of the line that makes an angle of $45^{\circ}$ with the $x$-axis and passes through the point $(3, -4)$?

$a$ and $b$ are the intercepts made by a line on the coordinate axes. If $3a = b$ and the line passes through $(1, 3)$,then the equation of the line is

The line passing through the points $(a, b)$ and $(-a, -b)$ passes through which of the following points?

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

Find the equation of a straight line that makes an intercept of $3$ units on the negative direction of the $y$-axis and is inclined at an angle of ${\tan ^{ - 1}}\left( {\frac{3}{5}} \right)$ with the $x$-axis.

The slope of a line passing through $P(2, 3)$ and intersecting the line $x + y = 7$ at a distance of $4$ units from $P$ is