Question

the following graph represents an inequality. select the ordered pairs which are solutions to it.
show your work here
(5, -2) (1, 7)
(0, 0) (2, -2)
(-2, 1) (6, -14)

Explanation:

Step1: Understand the Graph

The graph shows a shaded region (solution set) and a boundary line. To check if an ordered pair \((x,y)\) is a solution, we see if it lies in the shaded area.

Step2: Check Each Ordered Pair

• For \((5, -2)\): Plot \(x = 5\), \(y=-2\). It lies in the shaded region.
• For \((1, 7)\): Plot \(x = 1\), \(y = 7\). It lies in the shaded region.
• For \((0, 0)\): Plot \(x = 0\), \(y = 0\). It lies in the unshaded region (left of the boundary line), so not a solution.
• For \((2, -2)\): Plot \(x = 2\), \(y=-2\). It lies in the shaded region.
• For \((-2, 1)\): Plot \(x=-2\), \(y = 1\). It lies in the unshaded region, so not a solution.
• For \((6, -14)\): Plot \(x = 6\), \(y=-14\). It lies in the unshaded region (below the shaded area's lower boundary), so not a solution.

Answer:

The ordered pairs that are solutions are \((5, -2)\), \((1, 7)\), and \((2, -2)\).