Answer: g
Step-by-step explanation:
There are certain properties when working with graphs of inequalities. Notice that the graph was a solid line and not dashed. The only inequalities that can provide a solid line is ≤ or ≥. Knowing this fact can eliminate a, c, d, f, i.
The only options we have left are b, e, g, h, j.
B can be eliminated because x≥2 would generate a vertical line, which doesn't match the graph.
E states that 2y-x≤6. Solving this inequality can help figure out if it matches the graph.
[tex]2y-x\leq 6[/tex] [add x to both sides]
[tex]2y\leq x+6[/tex] [divide both sides by 2]
[tex]y\leq \frac{1}{2}x+3[/tex]
Notice that we end with ≤. If the graph has ≤, then the shaded region should be below the graph, which it is not. This eliminates e.
G states that 3y-4x≥12. Solving this inequality can help figure out if it matches the graph.
[tex]3y-4x\geq 12[/tex] [add 4x to both sides]
[tex]3y\geq 4x+12[/tex] [divide both sides by 3]
[tex]y\geq \frac{4}{3}x+4[/tex]
If the graph has ≥, then the shaded region should be above the graph, which it is. This makes g the correct answer.
H states that y≤-2x-4. If the graph has ≤, then the shaded region should be below the graph, which it is not. This eliminates h.
J states that 3x-1≥y. This translates to y≤3x-1. If the graph has ≤, then the shaded region should be below the graph, which it is not. This eliminates j.
Therefore, the final answer is g.
