To determine the correct linear inequality that matches the given graph, we need to consider the characteristics of the line and the shaded region.
The line is described as sloping steeply upward from the bottom left to the top right, which suggests a positive slope. The equation of a line in slope-intercept form is typically written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
From the options provided, it seems that the line likely has a slope of 2 (which corresponds to the coefficient of x in \( 2x \)), and the y-intercept appears to be positive (since the line goes upward and crosses the y-axis above the origin).
The shaded region is to the right of the line, which indicates that the area represented by the inequality is above the line. The choices involving \( y \geq \) or \( y > \) would indicate that the shaded region includes points at or above the line.
Among the options provided:
- \( y \geq 2x + 2 \) indicates that points on the line or above it are included (shaded above the line).
- \( y > 2x + 2 \) indicates points strictly above the line (not including the line itself).
- \( y \leq 2x + 2 \) would indicate points on or below the line which does not match.
- \( y < 2x + 2 \) indicates points strictly below the line which does not match.
Since the area to the right of the line is shaded, and if we assume the line is defined as \( y = 2x + 2 \), then:
- The correct choice is \( y \geq 2x + 2 \), as it includes points on the line and also above.
So, the final answer is:
y ≥ 2x + 2.