If the point (x, y) lies on the line joining the points (4, 3) and (– 1, – 3), then the relation between x and y is

The point (x, y) lies on the line joining the points (4, 3) and (– 1, – 3), if the area of triangle formed by these vertices is zero.

$\therefore \frac{1}{2}\left[x\left(3+3\right)+4\left(-3-y\right)-1\left(y-3\right)\right]=0$

$\Rightarrow 6x-12-4y-y+3=0$

$\Rightarrow 6x-5y=9$

Thus, the required relation between x and y is 6x – 5y = 9.