Let's break down the problem:

Naoya reads at a rate of 55 pages per hour. After 4 hours, he has 350 pages left. This means that in those 4 hours, he has read:

$55 \, \text{pages/hour} \times 4 \, \text{hours} = 220 \, \text{pages}.$

So, the total number of pages in the book is:

$\text{Total pages} = 220 \, \text{pages read} + 350 \, \text{pages left} = 570 \, \text{pages}.$

Now, we need to express the relationship between the number of hours passed ($x$) and the number of pages left to read ($y$).

After $x$ hours, the number of pages left to read can be calculated as:

$y = 570 - 55x.$

This equation represents a linear relationship because Naoya reads a fixed number of pages per hour, which results in a straight-line graph where the slope is $-55$ and the y-intercept is 570.

Key features of the graph:

• Slope: Since Naoya reads 55 pages per hour, the slope is $-55$ (negative because the number of pages left decreases over time).
• Y-intercept: The y-intercept is 570, which is the total number of pages in the book when $x = 0$ (before Naoya starts reading).
• Downward sloping: The graph should show a line that slopes downward because the number of pages left decreases over time.

Conclusion:

The correct graph should be a straight line starting at 570 on the y-axis (total pages) and sloping downward at a rate of 55 pages per hour.

---

Would you like more details on how to interpret or graph linear equations? Here are some related questions for further exploration:

1. How can we use the equation $y = 570 - 55x$ to predict how many pages are left after 6 hours?
2. How would the graph change if Naoya read at a rate of 60 pages per hour?
3. How can you calculate the y-intercept of a linear equation from a real-world scenario?
4. What is the relationship between the slope of a graph and the rate of change in real-world problems?
5. How do you convert this word problem into a different type of graph, such as a bar chart?

Tip: When interpreting word problems, always identify key details like rate of change, total amount, and how they relate to each other to form an equation.