If x >= 0 and y >= 0, how many lattice points does the line y = -2x + 78 pass through? (A lattice point is a point with integer coordinates.)
The line has a slope of -2
The y intercept is 78
The x intercept is 0 = -2x + 78 → 2x =78 → x = 39
So.....x int = (39,0) and y int = (0, 78)
The line will pass through a lattice point when x = any integer from 0 to 39 inclusive
The number of lattice points this line will pass through is given by
(39 - 0 ) + 1 =
40 lattice points