Question
Sean has 4 science fiction books for every 3 sports books. Which graph represents his book collection?
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 4) and (6, 8) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 5) and (6, 9) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (4, 3) and (8, 6) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 2) and (6, 4) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 4) and (6, 8) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 5) and (6, 9) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (4, 3) and (8, 6) are plotted.
On a coordinate plane, a graph titled Book Collection has science fiction on the x-axis and sports on the y-axis. Points (3, 2) and (6, 4) are plotted.
Answers
GPT-4o mini
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:
1. **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):
\[
y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 8, so does not fit)}
\]
2. **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):
\[
y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 9, so does not fit)}
\]
3. **Option 3:** Points (4, 3) and (8, 6)
- For (4, 3):
\[
y = \frac{3}{4}(4) = 3 \text{ (fits)}
\]
- For (8, 6):
\[
y = \frac{3}{4}(8) = 6 \text{ (fits)}
\]
4. **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.
\[
\frac{\text{Science Fiction}}{\text{Sports}} = \frac{4}{3}
\]
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:
1. **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):
\[
y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 8, so does not fit)}
\]
2. **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):
\[
y = \frac{3}{4}(6) = \frac{18}{4} = 4.5 \text{ (not 9, so does not fit)}
\]
3. **Option 3:** Points (4, 3) and (8, 6)
- For (4, 3):
\[
y = \frac{3}{4}(4) = 3 \text{ (fits)}
\]
- For (8, 6):
\[
y = \frac{3}{4}(8) = 6 \text{ (fits)}
\]
4. **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.