The graphical representation of the given inequality is required.
The correct option is A.
The function is [tex]y>\dfrac{1}{3}x-2[/tex]
Let us find the y and x intercepts of the function.
x intercept
[tex]y=0[/tex]
[tex]0=\dfrac{1}{3}x-2\\\Rightarrow x=6[/tex]
The x intercept is [tex](6,0)[/tex]
y intercept
[tex]x=0[/tex]
[tex]y=0-2\\\Rightarrow y=-2[/tex]
The y intercept is [tex](0,-2)[/tex]
Out of the options only A, B and D are possible answers as the points on the lines are represented correctly.
Let us find the shaded region by taking the origin as a reference point
[tex]0>0-2\\\Rightarrow 0>-2[/tex]
This statement is true so the shaded region will include the origin and exclude the line itself.
As the line is excluded the line will not be a solid line so option D is eliminated.
Since, A and B are possible answers and now we that the origin is in the shaded region the correct option is A.
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