In what ratio is the line segment joining the points $(-1, 1)$ and $(5, 7)$ divided by the line $x + y = 4$?

Find the equation of the line that bisects the line segment joining the points $(5, 3)$ and $(4, 4)$ and makes an angle of $45^{\circ}$ with the positive direction of the $x$-axis.

The equation of the line parallel to the line $2x - 3y = 1$ and passing through the midpoint of the line segment joining the points $(1, 3)$ and $(1, -7)$ is:

Let a line intersect the co-ordinate axes in points $A$ and $B$ such that the area of the triangle $OAB$ is $12$ sq. units. If the line passes through the point $(2,3)$,then the equation of the line is

The intercept of a line between the coordinate axes is divided by the point $(-5, 4)$ in the ratio $1 : 2$. The equation of the line will be:

The equation of the line passing through $(1, 2)$ and perpendicular to $3x + 4y + 5 = 0$ is