Answer:
Explanation:
The linear inequality represented by the graph is:
y > 3x + 2
In the given graph, the shaded area is above the line. This indicates that the values of y are greater than the corresponding values of 3x + 2.
Let's consider a point on the graph, such as (0,3). By substituting the x and y values into the inequality, we can verify that it satisfies the inequality:
3 > 3(0) + 2
3 > 2
Since 3 is greater than 2, the point (0,3) is within the shaded area above the line, supporting the inequality y > 3x + 2.
Please note that the other answer choices do not accurately represent the given graph:
- y < 3x + 2: This inequality would represent the area below the line, which is not the case in the given graph.
- y < One-thirdx + 2: This inequality represents a line with a different slope than the one shown in the graph, so it does not match the given graph.
- y > One-thirdx + 2: This inequality represents a line with a different slope than the one shown in the graph, so it does not match the given graph.
Therefore, the correct answer is y > 3x + 2, as it accurately represents the inequality for the shaded area above the line in the graph.