SOLUTION: A line segment joins the points ​(6​,15​) and ​(63,213​) in the Cartesian plane. Including its​ endpoints, how many lattice points does this l

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Question 1115030: A line segment joins the points ​(6​,15​) and ​(63,213​)
in the Cartesian plane. Including its​ endpoints, how many lattice points does this line segment​ contain? (A lattice point is a point with integer​ coordinates.)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The slope of the line is (213-15)/(63-6) = 198/57 = 66/19

There will be a lattice point for x values starting with 6 and incrementing by 19, until you reach 63:

6, 25, 44, 63

There are 4 lattice points, including the endpoints.