Answer:
The correct option is 3.
Step-by-step explanation:
It is given a graph of an inequality with a solid line through the points (0, −2) and (2, 1) with shading above the line.
The equation of a solid line is:
[tex]y-y_{1} = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } (x-x_{1})\\ y+2= \frac{1+2}{2-0}(x-0)\\ y+2= \frac{3}{2} x[/tex]
The y-intercept of the line is -2 and the shaded region is shading above the line. So, (0,0) must be lies in the shaded region.
Check the related equation by point (0,0).
0+2 =[tex]\frac{3}{2}(0)[/tex]
2 = 0
The statement is true if and only if the sign is greater than or equal instead of equal.
The required inequality is
[tex]y+2 \geq \frac{3}{2}x[/tex]
Multiply both sides by 2.
[tex]2y + 4 \geq 3x\\4\geq 3x-2y\\3x-2y \leq 4[/tex]
Therefore option 3 is correct.
Read to see a similar question about inequalities in the graph:
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