The problem involves Naoya reading a book at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. We are asked to choose a graph that represents the relationship between the number of pages left to read $y$ and the number of hours $x$.

Breakdown:

• Naoya's reading rate is 55 pages per hour.
• After 4 hours, there are 350 pages left to read.

Let’s develop a linear equation to describe the relationship between the number of pages left to read $y$ and the number of hours $x$.

1. Initial pages: At $x = 0$, Naoya has read 0 pages. After 4 hours, there are 350 pages left. Therefore, the total number of pages in the book is: $\text{Total Pages} = 350 + (55 \times 4) = 350 + 220 = 570.$

2. Equation of the line: Since Naoya reads 55 pages per hour, the number of pages left decreases by 55 pages for every hour that passes. The linear equation for the relationship between $y$ (pages left) and $x$ (hours) can be written as: $y = 570 - 55x.$ This is a line with a negative slope of $-55$, which means the graph should show a decreasing straight line.

Now, let's analyze the options:

• Correct option: The graph should show a straight line with a negative slope, starting from $y = 570$ when $x = 0$, and decreasing as $x$ increases. This is represented by option D.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can we interpret the slope of the graph in this problem?
2. How do we find the y-intercept of a linear equation from context?
3. Why is the relationship between time and pages left linear?
4. How would the graph change if the reading rate was different?
5. Can we determine how long it takes Naoya to finish the book?

Tip: The slope of a line in a word problem often represents a rate of change, like pages per hour in this case.