Final Answer:
c) y ≥ -4 It encompasses values greater than or equal to -4, and since the inequality 8 ≤ y > x + 2 operates in a different range on the y-axis, there's no intersection between them. Consequently, y ≥ -4 is the linear equality that does not share a solution set with the graphed linear inequality.
Explanation:
The linear inequality given is 8 ≤ y > x + 2. To find the linear equality that will not have a shared solution set with this inequality, let's examine the options. The inequality y ≥ -4 doesn't intersect with the graphed linear inequality. In the graphed inequality, y is restricted to be greater than or equal to 8 and must also be greater than x + 2. When comparing this with y ≥ -4, the latter doesn't intersect as it covers values above -4 on the y-axis, completely separate from the region defined by 8 ≤ y > x + 2. Thus, y ≥ -4 is the linear equality that won't share a solution set with the given inequality.
In the graphed inequality, the condition 8 ≤ y > x + 2 restricts y to values greater than or equal to 8 and greater than x + 2, which creates a distinct region in the coordinate plane. For the options provided, y ≥ -4 doesn't overlap with this region. It encompasses values greater than or equal to -4, and since the inequality 8 ≤ y > x + 2 operates in a different range on the y-axis, there's no intersection between them. Consequently, y ≥ -4 is the linear equality that does not share a solution set with the graphed linear inequality.