+0  
 
0
244
3
avatar

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+7155 
+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
 #1
avatar+7155 
+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+7155 
+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

12 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.