Which of the following inequalities is graphed in the xy-plane above?

Rationale

y ≥ -1/2x + 2

The inequality depicted in the graph has a slope of -1/2 and a y-intercept of 2, indicating that the region above the line is shaded, which corresponds to the inequality where y is greater than or equal to the line equation.

A (y ≥ 1/2x + 2) YOUR ANSWER

This inequality represents a line with a positive slope of 1/2, indicating that the region above the line would be shaded. However, this is inconsistent with the graph shown, where the line slopes downward, not upward.

B (y ≤ 1/2x + 2) YOUR ANSWER

Similar to option A, this choice has a positive slope of 1/2. It indicates shading below the line, which contradicts the graph that shows shading above a downward-sloping line.

C (y ≥ -1/2x + 2) CORRECT

This inequality has a slope of -1/2 and indicates that the area above the line is shaded. This matches the graph perfectly, confirming that y can take values greater than or equal to the line represented by -1/2x + 2.

D (y ≤ -1/2x + 2) YOUR ANSWER

This choice also features a slope of -1/2 but describes the region below the line. The graph clearly indicates that the shading is above the line, making this option incorrect.

Conclusion

The graph illustrates the inequality y ≥ -1/2x + 2, characterized by a negative slope and shading above the line. Options A and B incorrectly represent lines with positive slopes, while option D describes a region below the line. The correct interpretation aligns solely with option C, which accurately reflects the graphical representation shown.

Which of the following inequalities is graphed in the xy-plane above?

y ≥ -1/2x + 2

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