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

(Give your answer in "standard form" \(ax+by+c>0\) or  \(ax+by+c\geq0\) where a, b, and c are integers with no common factor greater than 1.)

 

HelpPLZ  Oct 18, 2018
edited by HelpPLZ  Oct 18, 2018
 #1
avatar+91112 
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Since this is a dashed line.....we will have either   "< "  or  " > "

 

The points (3,1)  and (1, -2)  are on the graph boundary 

 

The slope of this dashed line is  [ -2 - 1 ] / [ 1 - 3 ]   = -3 / -2  = 3 /2

 

The equation of the dashed line is

 

y = (3/2)( x - 1) - 2

 

y = (3/2)x - 3/2 - 2

 

 y = (3/2)x - 7/2

 

We will either have 

 

y < (3/2)x - 7/2     or   y > (3/2)x  - 7/2

 

(0 ,0)  is in the feasible  [ yellow ] region

 

Putting this coordinate into the second equation makes this inequality true

 

So....the inequality  is

 

y > (3/2)x - 7/2     multiply through by 2

2y > 3x - 7     subtract 2y from both sides

0 > 3x - 2y - 7     which is the same as

 

3x - 2y - 7 <  0

 

 

cool cool cool

CPhill  Oct 18, 2018

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