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

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

 Jun 1, 2021
 #1
avatar+119780 
+1

The  points   (-1,0)   and  (1,2)  are  on the inequality  boundary

 

Imagining the  boundary to to be  a solid line, the slope is  (  2-0 )  / (1 - -1)  =  2/2 =  1

 

And  the  equation  of this line using (  -1,0)  is

 

y = 1 ( x - - 1)

 

y =  x + 1

 

Bot  we  have  a dashed  line  so  the  equation  is either

 

y > x +  1                 or y <  x + 1

 

Note  that  (-2,0)  is in the  soltion region  and  this  satisfies    y  > x + 1

 

So      we  can rerrange  this  as

 

-x  + y   >   1  

 

Your  answer  might  also  be      -1  >  x - y   ⇒    x - y   <    -1    ⇒   x - y + 1  < 0  

 

 

cool cool cool

 Jun 1, 2021

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