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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.)

 Dec 12, 2020
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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

 

 

cool cool cool

 Dec 12, 2020

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