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avatar+144 

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  where \(ax+by+c\geq0\)  and \( a, b, \) and \(c\) are integers with no common factor greater than 1.)

HelpPLZ  Oct 8, 2018
 #1
avatar+92465 
+1

Note that the points  (5, - 2)  and  (4, -3)  would be on the graph  if we had a solid line

 

So....the slope would  be    [ -3 - -2 ] [ 4 -5]  = -1 /  -1     =  1

 

So...using   the point (5 , -2)  we can write the equation of this  "line"

 

We have

 

y  = 1 ( x -5)  - 2

 

y = x - 5  - 2

 

y = x - 7      or     x - 7   = y     subtract  y from both sides

 

x - y  - 7   = 0

 

However  ...we have a dashed line so we must have  a  >   or  <  insted of an  =

 

Note that the point  (0, 0)  is in the shaded region...so....testing this point in

 

x - y  - 7 >  0

 

0  - 0  - 7  >  0 

 

-7  > 0      not true

 

So...the equation must be

 

x - y  - 7  <  0

 

Here's the graph :  https://www.desmos.com/calculator/9jof1vd4lq

 

 

cool cool cool

CPhill  Oct 8, 2018
 #2
avatar+144 
+1

Thank you!

HelpPLZ  Oct 8, 2018

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