The equation of the line passing through $(4, -6)$ and making an angle of $45^\circ$ with the positive $x$-axis is:

The parallelism condition for two straight lines,one of which is specified by the equation $ax + by + c = 0$ and the other being represented parametrically by $x = \alpha t + \beta$ and $y = \gamma t + \delta$,is given by:

The equation of the line perpendicular to $x = c$ is

$A$ line passes through $(2,2)$ and is perpendicular to the line $3x+y=3$. Its $y$-intercept is:

The equation of the line passing through $(1, -2)$ and perpendicular to the $y$-axis is:

The intercept form of the equation of the straight line passing through the point $(4, -3)$ and perpendicular to the line passing through the points $(1, 1)$ and $(2, 3)$ is