The equation of the straight line making equal intercepts on the axes and passing through the point $(2, 4)$ is

The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1, 2)$ and $(-3, 5)$ in the ratio $4:3$ externally is

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:

If the line passing through the points $(4, 3)$ and $(2, \lambda)$ is perpendicular to the line $y = 2x + 3$,then find the value of $\lambda$.

Find the value of $x$ for which the points $(x, -1), (2, 1),$ and $(4, 5)$ are collinear.

The equation of the straight line passing through the point $(-5, 3)$ such that the portion of the line intercepted between the axes is divided by the point in the ratio $4:3$ (from the $X$-axis to the $Y$-axis) is...