Find the equation of the line passing through $(4, 6)$ and parallel to the line $3x - 7y + 2 = 0$.

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

The area of the triangle formed by the line $L$ with the coordinate axes is $12$ sq. units. If $L$ passes through the point $(12, 4)$ and the product $P$ of the $X$-intercept of $L$ and the square of the $Y$-intercept of $L$ is negative,then $P=$

Find the value of $k$,if the line joining the points $(2, k)$ and $(3, 7)$ is parallel to the line joining points $(-2, 1)$ and $(3, 0)$.

The equations of lines parallel to the coordinate axes and passing through the point $(5, -6)$ are

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