Sean has a ratio of 4 science fiction books for every 3 sports books. This can be represented mathematically as:
\[ \frac{\text{Science Fiction}}{\text{Sports}} = \frac{4}{3} \]
This implies that for every 4 science fiction books, there will be 3 sports books. We can express this ratio as a linear equation by letting \(x\) represent the number of science fiction books and \(y\) represent the number of sports books:
\[ y = \frac{3}{4}x \]
We can test each set of points given in the options to see which fits this equation:
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Option 1: Points (3, 4) and (6, 8)
- For (3, 4): \[ y = \frac{3}{4}(3) = \frac{9}{4} \text{ (not 4, so does not fit)} \]
- For (6, 8): \[ y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 8, so does not fit)} \]
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Option 2: Points (3, 5) and (6, 9)
- For (3, 5): \[ y = \frac{3}{4}(3) = \frac{9}{4} \text{ (not 5, so does not fit)} \]
- For (6, 9): \[ y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 9, so does not fit)} \]
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Option 3: Points (4, 3) and (8, 6)
- For (4, 3): \[ y = \frac{3}{4}(4) = 3 \text{ (fits)} \]
- For (8, 6): \[ y = \frac{3}{4}(8) = 6 \text{ (fits)} \]
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Option 4: Points (3, 2) and (6, 4)
- For (3, 2): \[ y = \frac{3}{4}(3) = \frac{9}{4} \text{ (not 2, so does not fit)} \]
- For (6, 4): \[ y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 4, so does not fit)} \]
The only set of points that corresponds to the ratio of 4 science fiction books for every 3 sports books is Option 3: Points (4, 3) and (8, 6). Thus, this graph represents Sean's book collection.