The inequality that matches the graph is:
[tex]2x-3y<7[/tex]
It is given that the line is a dashed line.
This means that the inequality is strict.
Also, the dashed line passes through (-10,-9) and (-1,-3) and (8,3)
Using two point formula we may find the equation of the line.
i.e. any line passing through two points (a,b) and (c,d) is calculated by using the equation:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(-10,-9) and (c,d)=(-1,-3)
The equation of line is:
[tex]y-(-9)=\dfrac{-3-(-9)}{-1-(-10)}\times (x-(-10))\\\\i.e.\\\\y+9=\dfrac{-3+9}{-1+10}\times (x+10)\\\\i.e.\\\\y+9=\dfrac{6}{9}\times (x+10)\\\\i.e.\\\\y+9=\dfrac{2}{3}\times (x+10)\\\\3(y+9)=2\times (x+10)\\\\3y+27=2x+20\\\\i.e.\\\\2x-3y=27-20\\\\i.e.\\\\2x-3y=7[/tex]
Also, the shaded region is above the line.
Hence, the inequality is:
[tex]2x-3y<7[/tex]
