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

 

http://latex.artofproblemsolving.com/9/7/8/978d0731638de9265a17eedb3bcb105f846ab6d7.png

 

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

 Jun 1, 2019
 #1
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Two points o the line are   3,1    and  1,-2        slope then equals    (y1-y2)/(x1-x2) = (1- -2) / (3-1) = 3/2

 

y = 3/2 x   +  b    find b by plugging in one of the points

 

1 = 3/2 (3) + b     b = -7/2

so the line equation is     y = 3/2 x - 7/2

The yellow shaded area is thus       y> 3/2 x - 7/2      Multiply through by 2

                                                        2y > 3x - 7           re-arrange

                                                        2y - 3x + 7 >0

 Jun 1, 2019
 #2
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Thanks

 Jun 1, 2019

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