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

Find the equation of the line passing through the point of intersection of the lines $4x + 7y - 3 = 0$ and $2x - 3y + 1 = 0$ that has equal intercepts on the axes.

In the equation $y - y_1 = m(x - x_1)$,if $m$ and $x_1$ are fixed and different lines are drawn for different values of $y_1$,then

If the straight line through the point $P(3, 4)$ makes an angle $\frac{\pi}{6}$ with the $x$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length $PQ$ 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 equation of the line passing through the point $(2,2)$ and cutting off intercepts on the axes whose sum is $9$.