Answer:
Explanation:
Based on the given information that the boundary line on the graph is represented by the equation 5x + 2y = 6 and is dashed, we can determine the correct inequality based on the shading.
Since the boundary line is dashed, it means that the inequality is not inclusive of the line itself. This implies that the shaded region will be either above or below the line, but not on the line.
To determine the direction of the shading, we can choose a point on either side of the line and substitute its coordinates into the equation to check if it satisfies the inequality. If it does, then that side is the solution region.
Let's take the point (0,0) as an example. Substituting these coordinates into the equation 5x + 2y = 6:
5(0) + 2(0) = 0 ≠ 6
Since (0,0) does not satisfy the equation, we can conclude that the solution region is not the side where (0,0) lies. Therefore, the shaded region is on the other side of the line.
If the shading is below the line, the inequality would be:
5x + 2y < 6
If the shading is above the line, the inequality would be:
5x + 2y > 6
Without further information or clarification about the shading, it is not possible to determine the exact inequality. However, it can be one of the above two options depending on the direction of the shading.