Question
Match the inequality to the graph.(4 points)
y ≤ ax + b
y <ax + b
y > ax + b
y ≥ax + b
a. dotted line going through (-5,-5) and (5,5) and upper left half highlighted red
b. dotted line going through (-5,-5) and (5,5) and bottom right half highlighted red
c. line going through (-5,-5) and (5,5) and bottom right half highlighted red
d. line going through (-5,-5) and (5,5) and upper left half highlighted red
y ≤ ax + b
y <ax + b
y > ax + b
y ≥ax + b
a. dotted line going through (-5,-5) and (5,5) and upper left half highlighted red
b. dotted line going through (-5,-5) and (5,5) and bottom right half highlighted red
c. line going through (-5,-5) and (5,5) and bottom right half highlighted red
d. line going through (-5,-5) and (5,5) and upper left half highlighted red
Answers
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Answered by
GPT-4o mini
To match the inequalities with their corresponding graphs, let's analyze what each inequality represents:
1. **y ≤ ax + b**: This inequality includes the line (solid line) and the region below it. The graph would be a solid line with the area below it highlighted red.
2. **y < ax + b**: This inequality does not include the line (dotted line) and the area below it is highlighted red. The graph would be a dotted line with the area below it shaded.
3. **y > ax + b**: This inequality does not include the line (dotted line) and the area above it is highlighted red. The graph would be a dotted line with the area above it shaded.
4. **y ≥ ax + b**: This inequality includes the line (solid line) and the area above it is highlighted red. The graph would be a solid line with the area above it shaded.
Now, let's match these descriptions with the graphs provided:
- **a**: Dotted line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches **y < ax + b**.
- **b**: Dotted line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches **y > ax + b**.
- **c**: Solid line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches **y ≤ ax + b**.
- **d**: Solid line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches **y ≥ ax + b**.
So the matches would be:
- **y ≤ ax + b**: **c**
- **y < ax + b**: **a**
- **y > ax + b**: **b**
- **y ≥ ax + b**: **d**
1. **y ≤ ax + b**: This inequality includes the line (solid line) and the region below it. The graph would be a solid line with the area below it highlighted red.
2. **y < ax + b**: This inequality does not include the line (dotted line) and the area below it is highlighted red. The graph would be a dotted line with the area below it shaded.
3. **y > ax + b**: This inequality does not include the line (dotted line) and the area above it is highlighted red. The graph would be a dotted line with the area above it shaded.
4. **y ≥ ax + b**: This inequality includes the line (solid line) and the area above it is highlighted red. The graph would be a solid line with the area above it shaded.
Now, let's match these descriptions with the graphs provided:
- **a**: Dotted line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches **y < ax + b**.
- **b**: Dotted line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches **y > ax + b**.
- **c**: Solid line going through (-5,-5) and (5,5) with bottom right half highlighted red. This matches **y ≤ ax + b**.
- **d**: Solid line going through (-5,-5) and (5,5) with upper left half highlighted red. This matches **y ≥ ax + b**.
So the matches would be:
- **y ≤ ax + b**: **c**
- **y < ax + b**: **a**
- **y > ax + b**: **b**
- **y ≥ ax + b**: **d**
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