+0  
 
+2
95
9
avatar+27 

Hello! I have two questions:

 

 

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

Graph:

https://latex.artofproblemsolving.com/a/2/9/a29ab229485ebb0bd55ba84d9b69637ee1b61804.png, or

 

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

Graph:

 

 

https://latex.artofproblemsolving.com/8/d/9/8d9bd0400837caad6ee0e3c73ac50b6260d13361.png, or

 Apr 17, 2021
 #1
avatar+121003 
+1

First one.....we  have  the  points  (0.1)  and ( -1,0)  on  the  dashed line

 

The slope is   ( 0-1)  /( -1 - 0)  =  -1/-1  = 1

 

Imagining  the dashed line to be solid, the  equation of this line is

 

y  = 1x + 1

 

y= x + 1

 

Since  we have  a dahed line....tehe inequality  is either

 

y < x + 1                or      y >  x + 1

 

The point (-1,1)  is  in the yellow region 

 

Putting this  into  both inequalities

 

1 < -1 + 1              1 >  - 1 + 1

1 < 0                      1  >  0

not true                     true

 

So...the correct inequality must be   y  > x + 1

 

 

cool cool cool

 Apr 17, 2021
 #2
avatar+27 
0

Sorry.... I dont think you're right... 

Batterydude6000  Apr 17, 2021
 #4
avatar+121003 
0

Here's the  graph of  y >  x + 1

 

https://www.desmos.com/calculator/b1v6lmicuv

 

 

cool cool cool

CPhill  Apr 17, 2021
 #3
avatar+121003 
0

Second one

 

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 

 

cool cool cool

 Apr 17, 2021
 #5
avatar+27 
+1

What in the world? I believe you, but the site says they are both wrong. Maybe bc of format?

Batterydude6000  Apr 17, 2021
 #6
avatar+27 
+1

OOOOOHHHH i know

 

 

(Give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where  a,b andc  are integers with no common factor other than 1.)

Batterydude6000  Apr 17, 2021
edited by Batterydude6000  Apr 17, 2021
 #7
avatar+121003 
+1

Answers in suggeted format

 

-x + y - 1  >   0   

 

And

 

-2x + y + 4   ≤  0

 

Hope  that'swhat you need....smiley smiley smiley

 

 

cool cool cool

 Apr 17, 2021
 #8
avatar+27 
0

1st one is correct... sadly, 2nd one is not.

 

 

 

 

TY THO

Batterydude6000  Apr 17, 2021
 #9
avatar+121003 
+1

Here is the  graph of  the second  :

 

https://www.desmos.com/calculator/tf81xtdbvp

 

I'm not  sure  of what they  want

 

  

 

cool cool cool

 Apr 17, 2021

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