In what ratio does the line $y - x + 2 = 0$ divide the line segment joining the points $(3, -1)$ and $(8, 9)$?

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 coordinates of the point where the line $3x - 2y - 6 = 0$ intersects the $Y$-axis.

Points $A$ and $B$ are in the first quadrant; point $O$ is the origin. If the slope of $OA$ is $1$,the slope of $OB$ is $7$,and $OA = OB = r$,then the slope of $AB$ is:

$A$ line is passing through the point $(4,3)$ and the sum of its intercepts made on the coordinate axes is $14$. Then an equation of that line is

The area of a triangle formed by a line with the coordinate axes is $49 \text{ sq. units}$. If the perpendicular drawn from the origin to this line makes an angle of $45^\circ$ with the positive $X$-axis, then the equation of the line is: