how to find number of points on the straight line which joins (-4,11) and (16,-1) whose coordinates are positive integers
The slope of the line segment is:
$\displaystyle \frac{12}{-20}=-\frac{3}{5}$
and so the lattice points are found by taking the given leftmost point and successively adding 5 to the x-coordinate and subtracting 3 from the y coordinate to get:
(-4,11), (1,8), (6,5), (11,2), (16,-1)