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If x >= 0 and y >= 0, how many lattice points does the line y = -x + 18 pass through? (A lattice point is a point with integer coordinates.)

 Oct 31, 2022
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First you look at the x and y intercepts, then you can make a list and find the # of terms in it.

The y-intercept is 18, when y = 0, x = 18, so the x-intercept is also 18.

That means that there is a lattice point at x = 0, x = 1, x = 2,..., x = 18. Altogether 19 lattice points.

 Oct 31, 2022

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