Question: Use the information given to complete the table. Then, write an equation in the form $y = kx$ to represent the situation.
Mario notices that four out of every seven books on his bookshelf are comic books.
How many comic books, $y$, are there for $x$ number of total books?
Enter the answer in each space provided. Use numbers instead of words.
top-left: text block about books/comic books and the equation $y = kx$; no graph shapes visible.
Total Books Comic Books
14 8
35 20
56 32
84 48
105 60
154 88
Equation
A two-column table is shown in the top-left/center-left of the page. The left column is labeled "Total Books" and the right column is labeled "Comic Books". The data pairs are $(14, 8)$, $(35, 20)$, $(56, 32)$, $(84, 48)$, $(105, 60)$, and $(154, 88)$. The equation box is located at the bottom-left.
1. **State the problem:** Mario notices that four out of every seven books on his bookshelf are comic books. We want to find the equation $y = kx$ where $y$ is the number of comic books and $x$ is the total number of books.
2. **Understand the ratio:** The ratio of comic books to total books is $\frac{4}{7}$. This means for every 7 books, 4 are comic books.
3. **Find the constant $k$:** Since $y = kx$, and $k$ represents the fraction of comic books per total books, we have:
$$k = \frac{4}{7}$$
4. **Write the equation:**
$$y = \frac{4}{7}x$$
5. **Check the table values:**
- For $x=14$, $y = \frac{4}{7} \times 14 = 8$ (matches table)
- For $x=35$, $y = \frac{4}{7} \times 35 = 20$ (matches table)
- For $x=56$, $y = \frac{4}{7} \times 56 = 32$ (matches table)
- For $x=84$, $y = \frac{4}{7} \times 84 = 48$ (matches table)
- For $x=105$, $y = \frac{4}{7} \times 105 = 60$ (matches table)
- For $x=154$, $y = \frac{4}{7} \times 154 = 88$ (matches table)
6. **Conclusion:** The equation that represents the number of comic books $y$ for $x$ total books is:
$$y = \frac{4}{7}x$$