Answer:
The correct answer is D. x + 3y > 10.
Step-by-step explanation:
Identify the boundary line: The graph depicts a solid line slating upwards from left to right. This line represents the equation that separates the solutions that satisfy the inequality from those that don't.
Shade the correct region: The shaded area extends above the boundary line. This indicates that for any point (x, y) that falls within the shaded region, the value of 3y + x will be greater than 10.
Test points: We can pick a point from the shaded region and another from the unshaded region to verify the inequality. For instance, let's consider points (2, 3) which lies in the shaded area. If we plug its coordinates into the inequality D. x + 3y > 10, we get: 2 + 3(3) > 10 which is true (11 > 10). On the other hand, if we take the point (1, 1) which falls below the line, we get: 1 + 3(1) = 4, which is not greater than 10.
Based on this analysis, we can confirm that the graph represents the inequality D. x + 3y > 10.
