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Find a linear inequality with the following solution set. Each grid line represents one unit.
https://latex.artofproblemsolving.com/b/d/c/bdc17544a660a2ede75d5c2642f86c2311ec1028.png

 
Guest Dec 6, 2017

Best Answer 

 #1
avatar+5552 
+1

 

The dotted line passes through  (4, -3)  and  (3, -4)  ,

 

so its slope   =   \(\frac{-4--3}{3-4}\)   =   \(\frac{-1}{-1}\)   =   1

 

Using the point  (4, -3)  and the slope  1 , the equation of the dotted line is

 

y - -3  =  1(x - 4)

y  =  x - 4 - 3

y  =  x - 7

 

We want our inequality's solution set to be all points on one side of this line. It will be either

 

y  >  x - 7     or     y  <  x - 7

 

Since we want  (0, 0)  to be a solution, let's test that point to find the right one.

 

0  >  0 - 7                            or                            0  <  0 - 7

0  >  -7      this is true.                                        0  < -7      this is false.

 

The inequality that has  (0, 0)  as a solution is the one we want....that is

 

y  >  x - 7

 
hectictar  Dec 7, 2017
Sort: 

3+0 Answers

 #1
avatar+5552 
+1
Best Answer

 

The dotted line passes through  (4, -3)  and  (3, -4)  ,

 

so its slope   =   \(\frac{-4--3}{3-4}\)   =   \(\frac{-1}{-1}\)   =   1

 

Using the point  (4, -3)  and the slope  1 , the equation of the dotted line is

 

y - -3  =  1(x - 4)

y  =  x - 4 - 3

y  =  x - 7

 

We want our inequality's solution set to be all points on one side of this line. It will be either

 

y  >  x - 7     or     y  <  x - 7

 

Since we want  (0, 0)  to be a solution, let's test that point to find the right one.

 

0  >  0 - 7                            or                            0  <  0 - 7

0  >  -7      this is true.                                        0  < -7      this is false.

 

The inequality that has  (0, 0)  as a solution is the one we want....that is

 

y  >  x - 7

 
hectictar  Dec 7, 2017
 #2
avatar
0

Question what is it in standard form?

 
Guest Dec 7, 2017
 #3
avatar+5552 
+1

y  >  x - 7

                         Add  7  to both sides.

y + 7  >  x

                        Subtract  y  from both sides.

7  >  x - y

 

x - y  <  7

 
hectictar  Dec 9, 2017

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