If (x, y) be on the line joining the two points

Since the point (x, y) lie on the line joining the points (1, −3) and (−4, 2); the area of triangle formed by these points is 0.

That is,

$\Delta=\frac{1}{2}\{x(-3-2)+1(2-y)-4(y+3)\}=0$

$-5 x+2-y-4 y-12=0$

$-5 x-5 y-10=0$

$x+y+2=0$

Thus, the result is proved.