The correct inequality for the graph is b. x≥2.
The graph is a vertical line at x=2.
The line extends infinitely upwards, indicating that all y values are greater than or equal to 2.
Therefore, the inequality that best describes the graph is x≥2.
Here's a breakdown of why the other inequalities are not correct:
a. y<−3: This describes a horizontal line below y=−3, not a vertical line.
c. 5x+10y>0: This inequality describes a shaded region above a certain line, not a vertical line.
d. y<x: This describes a line where y is always less than x, but the graph in the question shows y is always greater than or equal to x.
e. 2y−x≤6: This inequality describes a shaded region below a certain line, not a vertical line.
f. 6x+3y>9: This inequality describes a shaded region above a certain line, not a vertical line.
g. 3y−4x≥12: This inequality describes a shaded region above a certain line, not a vertical line.
h. y≤−2x−4: This describes a line with a negative slope, but the graph in the question is a vertical line.
i. 8x−6y<10: This inequality describes a shaded region below a certain line, not a vertical line.
j. 3x−1≥y: This describes a line with a positive slope, but the graph in the question is a vertical line.