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.)

gueesstt
May 4, 2018

#1**+1 **

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

CPhill
May 4, 2018