+610 If $x \geq 0$ and $y \geq 0$, how many lattice points does the line $y = -2x + 18$ pass through? (A lattice point is a point with integer coordinates.)
+128448 Since x , y ≥ 0.......we are only concerned with the lattice points intersected by the line in the first quadrant
So we have
y = -2x + 18
The line has a y intercept of 18.....so one lattice point is (0,18)
And letting y = 0, we can find the x intercept as
0 = -2x + 18
-18 = -2x
9 = x ....so a second lattice point is (9,0)
Now.....the slope is - 2.....which means that y will change by -2 when x changes by 1
So.....the other lattice points intercepted by the line are
(1, 16) (2, 14) (3, 12) (4, 10) (5, 8) (6, 6) ( 7, 4) (8,2)
So....10 lattice points
See the graph here :
https://www.desmos.com/calculator/climjgy2hb
