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Complete the sentences to describe the graph of the Inequality y – 4.5 ≥ 3(x + 2). For each drop-down, choose the correct word or phrase.
The boundary line of this inequality is ______, because the points on the boundary line are ______ the solution set.
The origin (0, 0) ______ in the shaded region.
To complete the sentences for the inequality ( y – 4.5 geq 3(x + 2) ):
1. The boundary line of this inequality is solid, because the points on the boundary line are included in the solution set.
2. The origin (0, 0) is not in the shaded region.
Explanation: The inequality is ( y geq 3x + 10.5 ) when rearranged. A solid line is used because the inequality is “greater than or equal to,” which includes points on the line. To determine if the origin is in the shaded region, you can test the point (0, 0) in the inequality. Since ( 0 geq 10.5 ) is false, the origin is not in the solution set.
Keep practicing, and feel free to ask for further clarification on math concepts!