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Find a linear inequality with the following solution set. Each grid line represents one unit.

(Give your answer in "standard form" \(ax+by+c>0\) or  \(ax+by+c\geq0\) where a, b, and c are integers with no common factor greater than 1.)

 

 Oct 18, 2018
 #1
avatar+98091 
+1

We have the points  (0,1)  and (1, 0)  on the graph boundary

 

The slope of the  line is given by  [ 0-1 ] / [ 1 -0 ] = -1 / 1  = -1

 

Writing an eauation of this line, we have

 

y = -x  + 1 

 

But  we either have the inequality

 

y ≥ -x + 1    or    y  ≤ -x + 1

 

Testing a point in the yellow region  ...I'll choose  (x, y) =  (0,0)  in both equations 

shows that the second equation is correct

 

Rearranging this we have

 

x + y - 1  ≤ 0

 

 

cool cool cool

 Oct 18, 2018

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