Sean has 4 science fiction books for every 3 sports books. Which graph represents his book collection?

Question

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.

Answer 1

To determine which graph represents Sean's book collection, we need to analyze the ratio of science fiction books to sports books. Sean has 4 science fiction books for every 3 sports books, which means that the ratio of science fiction books (S) to sports books (P) can be expressed as:

\[ \frac{S}{P} = \frac{4}{3} \]

This can also be rewritten in terms of coordinates, where we can express the relationship as:

\[ S = \frac{4}{3}P \]

We can calculate what the number of science fiction books would be for a few sample points representing the sports books:

1. For 3 sports books: \[ S = \frac{4}{3} \times 3 = 4 \] So the point would be (3, 4).

2. For 6 sports books: \[ S = \frac{4}{3} \times 6 = 8 \] So the point would be (6, 8).

Now, let’s compare these points with the options given:

• First option: Points (3, 4) and (6, 8) - This matches our calculations.
• Second option: Points (3, 5) and (6, 9) - This does not match.
• Third option: Points (4, 3) and (8, 6) - This does not represent the ratio given.
• Fourth option: Points (3, 2) and (6, 4) - This does not match the expected values.

Thus, the correct graph that represents Sean's book collection is the first option: points (3, 4) and (6, 8).