Line

Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.

Result

n =  9

Solution:

24x+36y720=0 y=23x+20 x>0y>0x,yN x>0x<30x,yN x{3,6,9,12,15,18,21,24,27} n=9 24x+36y-720 = 0 \ \\ y = -\dfrac23 x +20 \ \\ x>0 \land y>0 \land x,y\in N \ \\ x>0 \land x<30\land x,y\in N \ \\ x \in \{ 3, 6, 9, 12, 15, 18,21, 24, 27\} \ \\ n = 9 \ \\



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