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

    https://latex.artofproblemsolving.com/4/8/2/48234b947b623e95b3f920ee2e9ce6cb24dcfa4b.png     - Link to graph


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

 

Incorrect answers -  

y > 1/2x - 1/2

y+x<=1

 3x - 2y < 7

 x+y-1>0

 2x - 3y + 1 > 0

 (3x - 7) / 2 > 0

 Apr 18, 2021
 #1
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Shaded area is everything above the line but not including the line

line equation is  y = 1/2x - 1/2

 

answer   y > 1/2x - 1/2     <======== you have this listed as incorrect answer....but it IS correct !   You just need to complet the work to get it in the correct form....don't be a lazy person just looking for the answer !

 

y > 1/2x - 1/2

0 > 1/2x - 1/2 - y     multiply by 2

0 > x - 1 - 2y

  or        x - 2y -1 < 0

 

Here is a desmos graph:

 

https://www.desmos.com/calculator/acwb5p136t

 Apr 18, 2021
 #2
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I dont really understand

 Apr 18, 2021
 #3
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What part do you not understand? cheeky

ElectricPavlov  Apr 18, 2021
 #4
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How do I answer it? Like what are the steps to answer it?

 Apr 18, 2021
 #5
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Find the equation of the line.......Is this the problem you are having?  

ElectricPavlov  Apr 18, 2021
 #6
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Yes that is my problem

 Apr 18, 2021
 #7
avatar+31412 
+1

OK...here ya go ( image below)    Read carefully so you will understand .....

 

  Pick two convenient points on the line.....see the ones I picked?

   find the slope between these lines      slope = m = (y1-y2)/(x1-x2) =  (1-0) /( 3-1)   = 1/2

      so your line starts to look like    y = mx + b    <====== 'Slope-Intercept' form of a line

                                                        y = 1/2 x + b      now we need to calculate 'b'     use either of the points in the equation

                               using 3,1           1 = 1/2 (3) + b

                                                             b = - 1/2

                                       Now your line equation is  y = 1/2 x - 1/2

     the shaded area of the graph is everything GREATER than ( above ) the line

                               y > 1/2 x - 1/2     then re-arrange it into the form needed ( as I did in earlier post )  ......        helpful?

 

 

ElectricPavlov  Apr 18, 2021
 #8
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So that means x < 2y+1 is the answer? Am i correct?

 Apr 18, 2021
 #9
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+1

Answer was shown in above post

        x - 2y -1 < 0     <=========  This is the form requested in the Q

ElectricPavlov  Apr 18, 2021

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