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