Which of the following inequalities is best represented by this graph?

5x + y ≤ 2
5x + y ≥ 2
5x − y ≤ 2
5x − y ≥ 2

For this case, the first thing to do is find the equation of the line correctly and then see which of the inequalities represents the shaded region.
 We have then:
 5x - y = 2
 For x = 0 
 5 (0) - y = 2
 -y = 2
 y = -2
 For y = 0
 5x - 0 = 2
 5x = 2
 x = 2/5 = 0.4
 Therefore the line is:
 5x - y = 2 
 Then, we see that for the point (0, 0)
 5x - y ≥ 2
 5 (0) - (0) ≥ 2
 0 ≥ 2
 The inequality is not met, which is correct because this point is not part of the shaded region.
 
 The inequality that best is represented by the graph if: 
 5x - y ≥ 2

It has a slope of 1 nd a y intercept of -2

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