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Bot GPT 4-o mini To determine which graph shows a lower unit cost, we need to understand the slopes of the lines represented by the two graphs. The slope of a line in a coordinate plane often represents a rate, such as cost per unit.
1. **Line 1**:
- Passes through (0, 0) and (3, 6).
- The slope (m) can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
- For Line 1: \( m = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \).
2. **Line 2**:
- Passes through (0, 0) and (6, 3).
- Using the same slope formula:
- For Line 2: \( m = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2} \).
Now, comparing the slopes:
- Line 1 has a slope of 2, which indicates a cost of 2 units per item.
- Line 2 has a slope of \( \frac{1}{2} \), which indicates a lower cost of \( \frac{1}{2} \) unit per item.
Since a lower slope indicates a lower unit cost, **Line 2** shows a lower unit cost compared to Line 1.
Therefore, the answer is: **Graph 2 shows a lower unit cost.**