How many lattice points are there between (2,0) and (16,203)?
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Slope (m) = (y2 - y1) / (x2 - x1)
m = 203 / 14
General Equation of Line :
y - y1 = m * (x - x1)
=> y - 0 = (203/14)* (x - 2)
=> y = (203/14)* (x-2)
If(a,b) is a lattice point that joint the line segment,
Then
2 <= a <= 16 ----eq_1
b = (203/14) * (a-2)----- eq_2
From eq_2
203a - 14b = 406
29a - 2b = 58 (Divide by 7)
2b = 29a - 58 -----eq_3
if the value of a is even then only the eq_3 will be satisfied
Thus there will be a solution for every even a, 2 <= a <=16.
Therfore a total of 8 solutions
Number of Lattice is 8
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