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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  or  where   and  are integers with no common factor greater than 1.)

 Apr 17, 2021
 #1
avatar+33710 
+1

The shaded area is everything less than and INCLUDING the line ....    find the equation of the line to be

y = 2 x -4

 

shaded are is thus    y <= 2x-4

 Apr 17, 2021
 #2
avatar+50 
+1

CPhill already answered to the same one before here it is:

 

 

 

The points  ( 2,0)  and (0, -4)  are on the line

 

Slope  of line =  (-4 - 0) / ( 0 -2)  =  -4/-2   = 2

 

Equation of line  (using 0,-4)  is

 

y= 2x  -4

 

Since we have an solid line  the inequality is either

 

y ≤  2x - 4                  or  y  ≥  2x - 4

 

Note  that (3,1)  is in  the yellow region

 

If  we test  this point in both inequalities, note  that

 

1 ≤ 2(3)  - 4

 

1 ≤  6 - 4

 

1 ≤ 2  is true

 

So....the  correct  inequality is  y ≤  2x - 4 

 Apr 17, 2021

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